Minggu, 17 Agustus 2014

Tips Belajar Fisika

Bagaimana Belajar Fisika dan Matematika

John Baez

July 29, 2014


    Pengantar

    "Bagaimana belajar fisika dan matematika" - Judul artikel ini cukup menohok. Tentu saja setiap orang belajar sesuai dengan caranya sendiri-sendiri. Saya tidak tahu bagaimana seharusnya anda belajar matematika dan fisika. Namun saya anggap anda ke sini dalam rangka meminta nasehat, maka inilah sedikit nasehat dari saya soal bagaimana belajar matematika dan fisika.

    Saran saya ini ditujukan buat mereka yang tertarik dengan kajian fisika teoretis fundamental dan matematika terpakai di dalamnya. (yang di maksud dengan Fisika "fundamental" di sini adalah pencaharian hukum dasar tentang materi dan energi di alam semesta). Jika anda ingin melakukan eksperimen alih-alih teori, atau jika fisika bidang lain semisal fisika material mampat dan astrofisika, atau matematika yang tidak ada kaitannya dengan fisika, maka nasehat saya di sini tidak akan terlalu bermanfaat. Meskipun demikian ada saran penting juga di sini yang selayaknya anda perhatikan, namun setelahnya anda harus mencari pendapat dan nasehat dari yang lain menyangkut bidang anda.

    Belajar matematika dan fisika itu tidak akan pernah cukup bahkan jika sepanjang hayat. Asyiknya, belajar fisika dan matematika penuh dengan hal-hal yang menarik....tentu jika anda orang yang mempunyai cukup kesabaran. Banyak orang membaca buku populer tentang mekanika kuantum, lubang hitam, dan teorema Godel, dan sangat ingin segera mempelajarinya. Tanpa latar belakang yang memadai, mereka segera frustasi mempelajarinya---atau lebih buruk lagi menjadi patah semangat.

    Bahkan lebih bahaya lagi jika anda langsung ingin menerjunkan diri ke teori medan terpadu, superstring, atau M-teori. Tak ada juga orang yang bisa memastikan bahwa teori ini benar! dan sangat sulit membuktikan klaim-klaim teori tersebut hingga anda tahu apa sebenarnya yang diketahui orang lain.

    Jadi, khususnya ketika anda hendak belajar fisika, saya sarankan anda mulai dengan hal-hal yang lebih tidak wah yang kita tahu itu benar--sekurangnya sebagai sebuah pendekatan yang berguna, dan kemudian dengan latar belakang yang solid, pelan-pelan pengetahuan anda akan sampai ke frontier. Bahkan jika pada akhirnya anda menyerah di suatu titik anda setidaknya telah belajar beberapa hal.


    Web ini tidak mempunyai banyak link. Website ini (tempat penulis artikel menuangkan tulisannya) tidak menampilkan materi lanjut semacam matematika dan fisika lanjut--setidaknya hingga saat ini. Untuk mempelajari topik-topik ini anda mesti membaca banyak buku. Beberapa akan saya daftarkan di sini dan sebagian lagi dapat anda peroleh secara on line.

    Namun anda tidak dapat belajar fisika hanya dari baca buku-buku belaka! anda harus melakukan banyak perhitungan sendiri--atau melakukan eksperimen, tentu jika anda ingin melakukan fisika eksperimen. Buku Daras biasanya penuh dengan soal-soal, dan alangkah baiknya anda mengerjakan ini semua. Penting juga bagi anda untuk melakukan riset pribadi dan mengerjakannya sungguh-sungguh. Jika anda tidak mampu melakukan ini semua, tidak ada jalan melainkan harus mengambil kuliah di bidang fisika dan matematika. Keuntungan dari perkuliahan adalah anda dapat mendengar langsung perkuliahan, menemui mahasiswa dan profesor, dan melakukan hal-hal yang biasanya tidak akan anda lakukan--Misalkan akan lebih bekerja keras lagi dalam belajarnya.

    Sangatlah penting bagi anda untuk bertanya pada yang lain serta menjelaskannya sendiri--dua cara ini adalah besar sekali sumbangannya bagi pemahaman anda. Tak ada yang lebih merangsang belajar selain duduk bersama dengan teman di sebuah cafe, dengan buku catatan yang terbuka, serta bekerja bersama-sama secara teratur. Dua pikiran tentu lebih baik dari pada hanya satu pikiran.

    Namun jika anda tidak menemukan seorang teman di kota anda, ada cara lain untuk berdiskusi dengan orang lain yaitu secara on line. Dalam semua situasi, tentu penting bagi anda untuk memahami kebiasaan di situs tersebut sebelum terjun dalam diskusi. Sebagai contoh, langsung mencoba untuk memulai diskusi secara sporadis di sebuah website tanya jawab tidaklah bagus. Di sini ada beberapa pilihan web:
    Juga ada banyak Blog menarik, serta banyak buku matematika on line gratis free math books online.

    Akhirnya penting sekali untuk mengakui ketika anda berbuat kesalahan. Semua kita melakukan begitu banyak kesalahan ketika kita mempelajari sesuatu. Jika anda tidak bisa menerima ini, lambat laun anda akan menjadi  seorang yang dungu, yang menelorkan teori-teori bodoh, meskipun semua orang bisa melihat itu adalah kesalahan. Suatu tragedi jika anda sendiri tidak menyadarinya. Bahkan seorang profesor terkenal sekalipun dapat menjadi dungu ketika mereka berhenti mengakui kesalahan-kesalahannya.

    Untuk menghindari hal ini sangatlah baik jika anda menjelaskan sejelas mungkin apakah anda memang memahami sesuatu atau pengetahuan anda hanya perkiraan belaka, tidaklah terlalu buruk jika salah mengira bahwa anda sebenarnya kurang yakin dari awal. Namun jika anda begitu percaya diri dan terbukti belakangan anda keliru, maka anda akan terlihat tolol.

    Pungkas kata: stay humble, keep studying, and you'll keep making progress. Don't give up - the fun is in the process.

    Bagaimana caranya Belajar Fisika

    Ada 5 topik penting yang seyogyanya seorang fisikawan menguasainya:
    • Mekanika Klasik
    • Mekanika Statistik
    • Elektromagnetism
    • Relativitas Khusus
    dan
    • Mekanika Kuantum
    dalam urutan yang tak tentu. Sekali ilmu ini dikuasai, anda punya latar belakang untuk mempelajari dua teori terbaik:
    dan 
    Dan sekali anda memahami ini, anda siap untuk mengkaji usaha dewasa ini dalam menyatukan teori medan kuantum dan relativitas umum. Tampak ini usaha yang keras... memang demikian! Namun penuh juga dengan hal-hal yang menarik, terkadang juga melelahkan. Oleh karena itu bagus juga jika anda membaca buku sejarah fisika. . They're a nice change of pace, they're inspiring, and they can show you the "big picture" that sometimes gets hidden behind the thicket of equations. These are some of my favorites histories:
    • Emilio Segre, From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries, W. H. Freeman, New York, 1984.
    • Emilio Segre, From X-Rays to Quarks: Modern Physicists and Their Discoveries, W. H. Freeman, San Francisco, 1980.
    • Robert P. Crease and Charles C. Mann, The Second Creation: Makers of the Revolution in Twentieth-Century Physics, Rutgers University Press, New Brunswick, NJ, 1996.
    • Abraham Pais, Inward Bound: of Matter and Forces in the Physical World, Clarendon Press, New York, 1986. (More technical.)
    Next, here are some good books to learn "the real stuff". These aren't "easy" books, but they're my favorites.
    First, some very good general textbooks:
    • M. S. Longair, Theoretical Concepts in Physics, Cambridge U. Press, Cambrdige, 1986.
    • Richard Feynman, Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics, 3 volumes, Addison-Wesley, 1989. All three volumes are now free online.
    • Ian D. Lawrie, A Unified Grand Tour of Theoretical Physics, Adam Hilger, Bristol, 1990.
    Then, books that specialize on the 5 cornerstone topics I listed above: Classical mechanics:
    Statistical mechanics:
    Electromagnetism:
    Special relativity:
    Quantum mechanics:
    These should be supplemented by the general textbooks above, which cover all these topics. In particular, Feynman's Lectures on Physics are incredibly valuable.
    After you know this stuff well, you're ready for general relativity (which gets applied to cosmology) and quantum field theory (which gets applied to particle physics).     General relativity - to get intuition for the subject before tackling the details:
    General relativity - for when you get serious:

    General relativity - for when you get really serious:

    Cosmology:

    Quantum field theory - to get intuition for the subject before tackling the details:
    Quantum field theory - for when you get serious:
    Quantum field theory - two classic older texts that cover a lot of material not found in Peskin and Schroeder's streamlined modern presentation:
    • James D. Bjorken and Sidney D. Drell, Relativistic Quantum Mechanics, New York, McGraw-Hill, 1964.
    • James D. Bjorken and Sidney D. Drell, Relativistic Quantum Fields, New York, McGraw-Hill, 1965.
    Quantum field theory - for when you get really serious:
    • Sidney Coleman, Aspects of Symmetry, Cambridge U. Press, 1989. (A joy to read.)
    • Rudolf Haag, Local Quantum Physics: Fields, Particles, Algebras, Springer-Verlag, 1992.
    Quantum field theory - so even mathematicians can understand it:
    • Robin Ticciati, Quantum Field Theory for Mathematicians, Cambridge University Press, Cambridge, 1999.
    • Richard Borcherds and Alex Barnard, Lectures On Quantum Field Theory.
    Particle physics:
    • Kerson Huang, Quarks, Leptons & Gauge Fields, World Scientific, Singapore, 1982.
    • L. B. Okun, Leptons and Quarks, translated from Russian by V. I. Kisin, North-Holland, 1982. (Huang's book is better on mathematical aspects of gauge theory and topology; Okun's book is better on what we actually observe particles to do.)
    • T. D. Lee, Particle Physics and Introduction to Field Theory, Harwood, 1981.
    • K. Grotz and H. V. Klapdor, The Weak Interaction in Nuclear, Particle, and Astrophysics, Hilger, Bristol, 1990.
    While studying general relativity and quantum field theory, you should take a break now and then and dip into this book: it's a wonderful guided tour of the world of math and physics:
    • Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Knopf, New York, 2005.
    And then, some books on more advanced topics... The interpretation of quantum mechanics:
    • Roland Omnes, Interpretation of Quantum Mechanics, Princeton U. Press, Princeton, 1994.
    This is a reasonable treatment of an important but incredibly controversial topic. Warning: there's no way to understand the interpretation of quantum mechanics without also being able to solve quantum mechanics problems - to understand the theory, you need to be able to use it (and vice versa). If you don't heed this advice, you'll fall prey to all sorts of nonsense that's floating around out there. The mathematical foundations of quantum physics:
    • Josef M. Jauch, Foundations of Quantum Mechanics, Addison-Wesley, 1968. (Very thoughtful and literate. Get a taste of quantum logic.)
    • George Mackey, The Mathematical Foundations of Quantum Mechanics, Dover, New York, 1963. (Especially good for mathematicians who only know a little physics.)
    Loop quantum gravity and spin foams:
    • Carlo Rovelli, Quantum Gravity, Cambridge University Press, Cambridge, 2004.
    String theory:
    • Barton Zwiebach, A First Course in String Theory, Cambridge U. Press, Cambridge, 2004. (The best easy introduction.)
    • Michael B. Green, John H. Schwarz and Edward Witten, Superstring Theory (2 volumes), Cambridge U. Press, Cambridge, 1987. (The old testament.)
    • Joseph Polchinski, String Theory (2 volumes), Cambridge U. Press, Cambridge, 1998. (The new testament - he's got branes.)

    How to Learn Math

    Math is a much more diverse subject than physics, in a way: there are lots of branches you can learn without needing to know other branches first... though you only deeply understand a subject after you see how it relates to all the others! After basic schooling, the customary track through math starts with a bit of:
    and
    not necessarily in exactly this order. (For example, you need to know a little set theory and logic to really understand what a proof is.) Then, the study of math branches out into a dizzying variety of more advanced topics! It's hard to get the "big picture" of mathematics until you've gone fairly far into it; indeed, the more I learn, the more I laugh at my previous pathetically naive ideas of what math is "all about". But if you want a glimpse, try these books:
    • F. William Lawvere and Stephen H. Schanuel, Conceptual Mathematics: a First Introduction to Categories, Cambridge University Press, 1997. (A great place to start.)
    • Saunders Mac Lane, Mathematics, Form and Function, Springer-Verlag, New York, 1986. (More advanced.)
    • Jean Dieudonne, A Panorama of Pure Mathematics, as seen by N. Bourbaki, translated by I.G. Macdonald, Academic Press, 1982. (Very advanced - best if you know a lot of math already. Beware: many people disagree with Bourbaki's outlook.)
    I haven't decided on my favorite books on all the basic math topics, but here are a few. In this list I'm trying to pick the clearest books I know, not the deepest ones - you'll want to dig deeper later: Finite mathematics (combinatorics):
    Calculus:
    Multivariable calculus:
    Linear algebra:
    I don't have any favorite linear algebra books, so I'll just list some free ones:
    Ordinary differential equations - some free online books:
    Partial differential equations - some free online books:
    Complex analysis:
    Real analysis:
    Topology:
    Set theory and logic:
    Abstract algebra:
    I didn't like abstract algebra as an undergrad. Now I love it! Textbooks that seem pleasant now seemed dry as dust back then. So, I'm not confident that I could recommend an all-around textbook on algebra that my earlier self would have enjoyed. But, I would have liked these:
    Next, here are some books on topics related to mathematical physics. Out of laziness, I'll assume you're already somewhat comfortable with the topics listed above - yes, I know that requires about 4 years of full-time work! - and I'll pick up from there. Here's a good place to start:

    It's also good to get ahold of these books and keep referring to them as needed:
    Here's a free online reference book that's 787 pages long:
    Here are my favorite books on various special topics:
    Group theory in physics:
    • Shlomo Sternberg, Group Theory and Physics, Cambridge University Press, 1994.
    • Robert Hermann, Lie Groups for Physicists, Benjamin-Cummings, 1966.
    • George Mackey, Unitary Group Representations in Physics, Probability, and Number Theory, Addison-Wesley, Redwood City, California, 1989.
    Lie groups, Lie algebras and their representations - in rough order of increasing sophistication:
    • Brian Hall, Lie Groups, Lie Algebras, and Representations, Springer Verlag, Berlin, 2003.
    • William Fulton and Joe Harris, Representation Theory - a First Course, Springer Verlag, Berlin, 1991. (A friendly introduction to finite groups, Lie groups, Lie algebras and their representations, including the classification of simple Lie algebras. One great thing is that it has lots of pictures of root systems, and works slowly up a ladder of examples of these before blasting the reader with abstract generalities.)
    • J. Frank Adams, Lectures on Lie Groups, University of Chicago Press, Chicago, 2004. (A very elegant introduction to the theory of semisimple Lie groups and their representations, without the morass of notation that tends to plague this subject. But it's a bit terse, so you may need to look at other books to see what's really going on in here!)
    • Daniel Bump, Lie Groups, Springer Verlag, Berlin, 2004. (A friendly tour of the vast and fascinating panorama of mathematics surrounding groups, starting from really basic stuff and working on up to advanced topics. The nice thing is that it explains stuff without feeling the need to prove every statement, so it can cover more territory.)
    Geometry and topology for physicists - in rough order of increasing sophistication:
    • Gregory L. Naber, Topology, Geometry and Gauge Fields: Foundations, Springer Verlag, Berlin, 1997.
    • Chris Isham, Modern Differential Geometry for Physicists, World Scientific Press, Singapore, 1999. (Isham is an expert on general relativity so this is especially good if you want to study that.)
    • Harley Flanders, Differential Forms with Applications to the Physical Sciences, Dover, New York, 1989. (Everyone has to learn differential forms eventually, and this is a pretty good place to do it.)
    • Charles Nash and Siddhartha Sen, Topology and Geometry for Physicists, Academic Press, 1983. (This emphasizes the physics motivations... it's not quite as precise at points.)
    • Mikio Nakahara, Geometry, Topology, and Physics, A. Hilger, New York, 1990. (More advanced.)
    • Charles Nash, Differential Topology and Quantum Field Theory, Academic Press, 1991. (Still more advanced - essential if you want to understand what Witten is up to.)
    Geometry and topology, straight up:
    • Victor Guillemin and Alan Pollack, Differential Topology, Prentice-Hall, Englewood Cliffs, 1974.
    • B.A. Dubrovin, A.T. Fomenko, and S.P. Novikov, Modern Geometry - Methods and Applications, 3 volumes, Springer Verlag, Berlin, 1990. (Lots of examples, great for building intuition, some mistakes here and there. The third volume is an excellent course on algebraic topology from a geometrical viewpoint.)
    Algebraic topology:
    Knot theory:
    • Louis Kauffman, On Knots, Princeton U. Press, Princeton, 1987.
    • Louis Kauffman, Knots and Physics, World Scientific, Singapore, 1991.
    • Dale Rolfsen, Knots and Links, Publish or Perish, Berkeley, 1976.
    Geometrical aspects of classical mechanics:
    • V. I. Arnold, Mathematical Methods of Classical Mechanics, translated by K. Vogtmann and A. Weinstein, 2nd edition, Springer-Verlag, Berlin, 1989. (The appendices are somewhat more advanced and cover all sorts of nifty topics.)
    Analysis and its applications to quantum physics:
    • Michael Reed and Barry Simon, Methods of Modern Mathematical Physics (4 volumes), Academic Press, 1980.
    Homological algebra:
    • Joseph Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979. (A good introduction to an important but sometimes intimidating branch of math.)
    • Charles Weibel, An Introduction to Homological Algebra, Cambridge U. Press, Cambridge, 1994. (Despite having the same title as the previous book, this goes into many more advanced topics.)

    I have always imagined that Paradise will be a kind of library. - Jorge Luis Borges

     Berikut artikel yang juga bagus berisi saran dari Prof. T'hooft seorang nobelis fisika dari Belanda

    How to become a
    GOOD Theoretical Physicist

    This is a web site (under construction) for young students - and anyone else - who are (like me) thrilled by the challenges posed by real science, and who are - like me - determined to use their brains to discover new things about the physical world that we are living in. In short, it is for all those who decided to study theoretical physics, in their own time.

    It so often happens that I receive mail - well-intended but totally useless - by amateur physicists who believe to have solved the world. They believe this, only because they understand totally nothing about the real way problems are solved in Modern Physics. If you really want to contribute to our theoretical understanding of physical laws - and it is an exciting experience if you succeed! - there are many things you need to know. First of all, be serious about it. All necessary science courses are taught at Universities, so, naturally, the first thing you should do is have yourself admitted at a University and absorb everything you can. But what if you are still young, at School, and before being admitted at a University, you have to endure the childish anecdotes that they call science there? What if you are older, and you are not at all looking forward to join those noisy crowds of young students?

    It should be possible, these days, to collect all knowledge you need from the internet. Problem then is, there is so much junk on the internet. Is it possible to weed out those very rare pages that may really be of use? I know exactly what should be taught to the beginning student. The names and topics of the absolutely necessary lecture courses are easy to list, and this is what I have done below. It is my intention to search on the web where the really useful papers and books are, preferably downloadable as well. This way, the costs of becoming a theoretical physicist should not exceed much the price of a computer with internet connection, a printer, and lots of paper and pens. Unfortunately, I still have to recommend to buy text books as well, but it is harder to advise you here; perhaps in a future site. Let’s first limit ourselves to the absolute minimum. The subjects listed below must be studied. Any omission will be punished: failure. Do get me right: you don’t have to believe anything you read on faith - check it. Try alternative approaches, as many as you can. You will discover, time and again, that really what those guys did indeed was the smartest thing possible. Amazing. the best of the texts come with exercises. Do them. find out that you can understand everything. Try to reach the stage that you discover the numerous misprints, tiny mistakes as well as more important errors, and imagine how you would write those texts in a smarter way.

    I can tell you of my own experiences. I had the extreme luck of having excellent teachers around me. That helps one from running astray. It helped me all the way to earn a Nobel Prize. But I didn’t have internet. I am going to try to be your teacher. It is a formidable task. I am asking students, colleagues, teachers to help me improve this site. It is presently set up only for those who wish to become theoretical physicists, not just ordinary ones, but the very best, those who are fully determined to earn their own Nobel Prize. If you are more modest than that, well, finish those lousy schools first and follow the regular routes provided by educators and specialized -gogues who are so damn carefully chewing all those tiny portions before feeding them to you. This is a site for ambitious people. I am sure that anyone can do this, if one is gifted with a certain amount of intelligence, interest and determination. Now, here begins the serious stuff. Don’t complain that it looks like being a lot. You won’t get your Nobel Prize for free, and remember, all of this together takes our students at least 5 years of intense study (at least one reader was surprised at this statement, saying that (s)he would never master this in 5 years; indeed, I am addressing people who plan to spend most of their time to this study). More than rudimentary intelligence is assumed to be present, because ordinary students can master this material only when assisted by patient teachers. It is necessary to do exercises. Some of the texts come with exercises. Do them, or better, invent your own exercises. Try to outsmart the authors, but please refrain from mailing to me your alternative theories until you have studied the entire lot; if you do this well you will discover that many of these authors were not so stupid after all.

    Theoretical Physics is like a sky scraper. It has solid foundations in elementary mathematics and notions of classical (pre-20th century) physics. Don’t think that pre-20th century physics is “irrelevant” since now we have so much more. In those days, the solid foundations were laid of the knowledge that we enjoy now. Don’t try to construct your sky scraper without first reconstructing these foundations yourself. The first few floors of our skyscraper consist of advanced mathematical formalisms that turn the Classical Physics theories into beauties of their own. They are needed if you want to go higher than that. So, next come many of the other subjects listed below. Finally, if you are mad enough that you want to solve those tremendously perplexing problems of reconciling gravitational physics with the quantum world, you end up studying general relativity, superstring theory, M-theory, Calabi-Yau compactification and so on. That’s presently the top of the sky scraper. There are other peaks such as Bose-Einstein condensation, fractional Hall effect, and more. Also good for Nobel Prizes, as the past years have shown. A warning is called for: even if you are extremely smart, you are still likely to get stuck somewhere. Surf the net yourself. Find more. Tell me about what you found. If this site has been of any help to someone while preparing for a University study, if this has motivated someone, helped someone along the way, and smoothened his or her path towards science, then I call this site successful. Please let me know. Here is the list.

    Note that this site NOT meant to be very pedagogical. I avoid texts with lots of colorful but distracting pictures from authors who try hard to be funny. Also, the subjects included are somewhat focused towards my own interests.

    LIST OF SUBJECTS, IN LOGICAL ORDER ARE ON THE SIDE. (Not everything has to be done in this order, but this approximately indicates the logical coherence of the various subjects. Some notes are at a higher level than others).

    Languages

    English is a prerequisite. If you haven’t mastered it yet, learn it. You must be able to read, write, speak and understand English, but you don’t have to be perfect here. The lousy English used in this text is mine. That’s enough. All publications are in English. Note the importance of being able to write in English. Sooner or later you will wish to publish your results. People must be able to read and understand your stuff.
    French, German, Spanish and Italian may be useful too, but they are not at all necessary. They are nowhere near the foundations of our sky-scraper, so don’t worry. You do need the Greek alphabet. Greek letters are used a lot. Learn their names, otherwise you make a fool of yourself when giving an oral presentation.
    If you have managed to read and follow this webpage so far, you probably don't need a first course in English. However, you want to be precise in your academic publications. You never want to be misunderstood, after all. Below, you will find several resources that are intended to be helpful for readers of various levels and with various requirements.
    Dictionaries Grammar Vocabulary Punctuation Writing Pronunciation
     
     

    Primary Mathematics

    Now, first things first. Are you comfortable with numbers, adding, subtracting, square roots, etc.?
    • Natural numbers: 1, 2, 3, …
    • Integers: …, -3, -2, -1, 0, 1, 2, …
    • Rational numbers (fractions): 12, 14, 34, 23791773, …
    • Real numbers: Sqrt(2) = 1.4142135… , π = 3.14159265… , e = 2.7182818…, …
    • Complex numbers: 2+3i, eia= cos(a) + i sin( a), … they are very important!
    • Set theory: open sets, compact spaces. Topology.You may be surprised to learn that they do play a role indeed in physics!
    • Algebraic equations. Approximation techniques. Series expansions: the Taylor series.
    • Solving equations with complex numbers. Trigonometry: sin(2x)=2sin x cos x, etc.
    • Infinitesimals. Differentiation. Differentiate basic functions (sin, cos, exp).
    • Integration. Integrate basic functions, when possible. Differential equations. Linear equations.
    • The Fourier transformation. The use of complex numbers. Convergence of series.
    • The complex plane. Cauchy theorems and contour integration (now this is fun).
    • The Gamma function (enjoy studying its properties).
    • Gaussian integrals. Probability theory.
    • Partial differential equations. Dirichlet and Neumann boundary conditions.


    This is for starters. Some of these topics actually come as entire lecture courses. Much of those are essential ingredients of theories in Physics. You don’t have to finish it all before beginning with what follows next, but remember to return to those subjects skipped during the first round.

    Classical Mechanics

    • Static mechanics (forces, tension); hydrostatics. Newton’s Laws
    • The elliptical orbits of planets. The many-body system
    • The action principle. Hamilton’s equations. The Lagrangean. (Don’t skip - extremely important!)
    • The harmonic oscillator. The pendulum
    • Poisson’s brackets
    • Wave equations. Liquids and gases. The Navier-Stokes equations. Viscosity and friction

    Optics

    • Fraction and reflection
    • Lenses and mirrors
    • The telescope and the microscope
    • Introduction to wave propagation
    • Doppler effect
    • Huijgens’ principle of wave superposition
    • Wave fronts
    • Caustics

    Statistical Mechanics & Thermodynamics

    • The first, second and third laws of thermodynamics
    • The Boltzmann distribution
    • The Carnot cycle. Entropy. Heat engines
    • Phase transitions. Thermodynamical models
    • The Ising Model (postpone techniques to solve the 2-dimensional Ising Model to later)
    • Planck’s radiation law (as a prelude to Quantum Mechanics)

    Electronics

    (Only some very basic things about electronic circuits)
    • Ohm’s law, capacitors, inductors, using complex numbers to calculate their effects
    • Transistors, diodes (how these actually work comes later)

    Electromagnetism

    Maxwell’s Theory for electromagnetism:

    Computational Physics

    Even the pure sang theorist may be interested in some aspects of Computational physics.

    Quantum Mechanics (Non-relativistic)

    • Bohr’s atom
    • DeBroglie’s relations (Energy-frequency, momentum-wave number)
    • Schrödinger’s equation (with electric potential and magnetic field)
    • Ehrenfest’s theorem
    • A particle in a box
    • The hydrogen atom, solved systematically. The Zeeman effect. Stark effect
    • The quantum harmonic oscillator
    • Operators: energy, momentum, angular momentum, creation and annihilation operators
    • Their commutation rules
    • Introduction to quantum mechanical scattering. The S-matrix. Radio-active decay

    Atoms & Molecules

    • Chemical binding
    • Orbitals
    • Atomic and molecular spectra
    • Emission and absorption of light
    • Quantum selection rules
    • Magnetic moments

    Solid State Physics

    • Crystal groups
    • Bragg reflection
    • Dielectric and diamagnetic constants
    • Bloch spectra
    • Fermi level
    • Conductors, semiconductors and insulators
    • Specific heat
    • Electrons and holes
    • The transistor
    • Supraconductivity
    • Hall effect

    Nuclear Physics

    • Isotopes
    • Radio-activity
    • Fission and fusion
    • Droplet model
    • Nuclear quantum numbers
    • Magic nuclei
    • Isospin
    • Yukawa theory

    Plasma Physics

    • Magneto-hydrodynamics
    • Alfvén waves

    Advanced Mathematics

    • Group theory, and the linear representations of groups
    • Lie group theory
    • Vectors and tensors
    • More techniques to solve (partial) differential and integral equations
    • Extremum principle and approximation techniques based on that
    • Difference equations
    • Generating functions
    • Hilbert space
    • Introduction to the functional integral

    Special Relativity

    • The Lorentz transformation
    • Lorentz contraction, time dilatation
    • E = mc2
    • 4-vectors and 4-tensors
    • Transformation rules for the Maxwell field
    • Relativistic Doppler effect

    Advanced Quantum Mechanics

    • Hilbert space
    • Atomic transitions
    • Emission and absorption of light
    • Stimulated emission
    • Density matrix
    • Interpretation of QM
    • The Bell inequalities
    • Towards relativistic QM: The Dirac equation, finestructure
    • Electrons and positrons
    • BCS theory for supraconductivity
    • Quantum Hall effect
    • Advanced scattering theory
    • Dispersion relations
    • Perturbation expansion
    • WKB approximation, Extremum principle
    • Bose-Einstein condensation
    • Superliquid helium

    Phenomenology

    Subatomic particles (mesons, baryons, photons, leptons, quarks) and cosmic rays; property of materials and chemistry; nuclear isotopes; phase transitions; astrophysics (planetary system, stars, galaxies, red shifts, supernovae); cosmology (cosmological models, inflationary universe theories, microwave background radiation); detection techniques.

    General Relativity

    • The metric tensor
    • Space-time curvature
    • Einstein’s gravity equation
    • The Schwarzschild black hole
    • Reissner-Nordström black hole
    • Periastron shift
    • Gravitational lensing
    • Cosmological models
    • Gravitational radiation

    Cosmology

    Cosmology and Astrophysics are relatively young branches of science where a lot is happening. It is recommended to take notice of these important subjects, and devote time on them according to your taste. Indeed you must know that there is feedback from cosmology, astrophysics and astroparticle physics in solving various physics questions. But I can go on this way: what about the physics of other special branches of science: biophysics, geophysics, the physics of music, ... I encourage you to search for other such subjects of interest on the web.


    Astro-Physics & Astronomy

    Cosmology and Astrophysics are relatively young branches of science where a lot is happening. It is recommended to take notice of these important subjects, and devote time on them according to your taste. Indeed you must know that there is feedback from cosmology, astrophysics and astroparticle physics in solving various physics questions. But I can go on this way: what about the physics of other special branches of science: biophysics, geophysics, the physics of music, ... I encourage you to search for other such subjects of interest on the web

    Quantum Field Theory

    • Classical fields: Scalar, Dirac-spinor, Yang-Mills vector fields.
    • Interactions, perturbation expansion. Spontaneous symmetry breaking, Goldstone mode, Higgs mechanism.
    • Particles and fields: Fock space. Antiparticles. Feynman rules. The Gell-Mann-Lévy sigma model for pions and nuclei. Loop diagrams. Unitarity, Causality and dispersion relations. Renormalization (Pauli-Villars; dimensional ren.) Quantum gauge theory: Gauge fixing, Faddeev-Popov determinant, Slavnov identities, BRST symmetry. The renormalization group. Asymptotic freedom.
    • Solitons, Skyrmions. Magnetic monopoles and instantons. Permanent quark confinement mechanism. The 1/N expansion. Operator product expansion. Bethe-Salpeter equation. Construction of the Standard Model. P and CP violation. The CPT theorem. Spin and statistics connection. Supersymmetry.

    Supersymmetry & Supergravity

    ...


    Astro Particle Physics

    ...


    Super String Theory


    Texts & Other Resources

    There are numerous good books on all sorts of topics in Theoretical Physics. Here are a few:
    Classical Mechanics:
    • Classical Mechanics - 3rd ed. - Goldstein, Poole & Safko
    • Classical dynamics: a contemporary approach - Jorge V. José, Eugene J. Saletan
    • Classical Mechanics - Systems of Particles and Hamiltonian Dynamics - W. Greiner
    • Mathematical Methods of Classical Mechanics, 2nd ed. - V.I. Arnold
    • Mechanics 3rd ed. - L. Landau, E. Lifshitz

    Statistical Mechanics:
    • L. E. Reichl: A Modern Course in Statistical Physics, 2nd ed.
    • R. K. Pathria: Statistical Mechanics
    • M. Plischke & B. Bergesen: Equilibrium Statistical Physics
    • L. D. Landau & E. M. Lifshitz: Statistical Physics, Part 1
    • S.-K. Ma, Statistical Mechanics, World Scientific

    Quantum Mechanics:
    • Quantum Mechanics - an Introduction, 4th ed. - W. Greiner
    • R. Shankar, Principles of Quantum Mechanics, Plenum
    • Quantum Mechanics - Symmetries 2nd ed. - W. Greiner, B. Muller
    • Quantum Mechanics - Vol 1&2 - Cohen-TannoudjiJ.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley

    Electrodynamics:
    • J.D. Jackson, Classical Electrodynamics, 3rd ed., Wiley & Sons.
    • Electromagnetic Fields And Waves - lorrain and corson
    • Classical Electrodynamics - W. Greiner
    • Introduction to Electrodynamics - D. Griffiths
    • Quantum Electrodynamics - 3rd ed., - W. Greiner, J. Reinhardt

    Optics:
    • Principles of Optics - M.Born, E. Wolf
    • Principles Of Nonlinear Optics - Y. R. Shen

    Thermodynamics:
    • Thermodynamics and an Introduction to Thermostatistics 2ed - H. Callen
    • Thermodynamics and statistical mechanics - Greiner, Neise, Stoecker

    Solid State Physics:
    • Solid State Physics - Ashcroft, Neil W, Mermin, David N
    • Introduction to Solid State Physics 7th edition- Kittel, Charles

    Special Relativity:
    • Classical Mechanics - Point Particles And Relativity - W. Greiner
    • Introduction to the theory of relativity and the principles of modern physics - H. Yilmaz

    General Relativity:
    • J.B. Hartle, Gravity, An Introduction to Einstein’s General Relativity, Addison Wesley, 2003.
    • T.-P. Cheng, Relativity, Gravitation and Cosmology, A Basic Introduction, Oxford Univ. Press, 2005.

    Particle Physics:
    • Introduction to Elementary Particles - D. Griffiths
    • Fundamentals in Nuclear Physics - From Nuclear Structure to Cosmology - Basdevant, Rich, Spiro

    Field Theory:
    • B. de Wit & J. Smith, Field Theory in Particle Physics, North-Holland
    • C. Itzykson & J.-B. Zuber, Quantum Field Theory, McGraw-Hill.

    String Theory:
    • Barton Zwiebach, A First Course in String Theory, Cambridge Univ. Press, 2004
    • M.B. Green, J.H. Schwarz & E. Witten, Superstring theory, Vols. I & II, Cambridge Univ. Press

    Cosmology:
    • An Introduction to cosmology, 3rd Ed – Roos
    • Relativity, thermodynamics, and cosmology - Tolman R.C.

    General:
    • J.B. Marion & W.F. Hornyak, Principles of Physics, Saunders College Publishing, 1984, ISBN 0-03-049481-8
    • H. Margenau and G.M. Murphy, The Mathematics of Physics and Chemistry, D. v.Nostrand Comp.
    • R. Baker, Linear Algebra, Rinton Press

    Find lists of other useful textbooks here: Mathematics, Physics (most of these are rather for amusement than being essential for understanding the World), or a little bit more seriously: Physics.


    Responses & Questions

    Please direct any questions, comments or suggestions to Nava Gaddam (gaddam@uu.nl).
    There already has been some response. I thank: Rob van Linden, Robert Tough, Thuy Nguyen, Tina Witham, Jerry Blair, Jonathan Martin, David Cuthbertson, Trent Strong, and many others.
    Mr. Hisham Kotry came with an important question:
    "… You sketch the path for potential students through the forest of college level physics… Two years ago I decided to self-study theoretical physics by following the syllabus of a renown university and the advice from your page and now I’m half-way through the journey but I was wondering about what happens next? Quoting you from the former page "In short, it is for all those who decided to study theoretical physics, in their own time.", Do you know of anyone who got tenure at a physics department or any research institute based on studies he did in his own time without holding a university degree?"
    This is not so easy to answer, unfortunately. What I can say, is:
    Eventually, whether you like it or not, you will have to obtain some University degree, if you wish a self-supporting career in theoretical Physics. One possibility is to follow a Master course such as the one offered by our University. I don’t know about your qualifications, but I suspect that, with enough determination, you may be able to comply.
    This is not a burocratic argument but a very practical one. It is also advisable not to wait until you think your self-study is completed. You must allow your abilities to be tested, so that you get the recognition that you may well deserve. Also, I frequently meet people who get stuck at some point. Only by intense interactions with teachers and peers one can help oneself across such barriers. I have not yet met anyone who could do the entire study all by him/herself without any guidance. If you really think you have reached a professional level in your studies, you can try to get admitted to schools, conferences and workshops in topics of your interest.
    3/04/06: Message received from John Glasscock, Bloomington, IN:
    The only one I know of currently is John Moffatt at U Toronto, who was a student of Abdus Salam at Imperial College, London. He started life as a painter in Paris, had no undergraduate degree, taught himself, corresponded with Einstein, and was admitted, based on his demonstrated original work, at IC. (Source: João Magueijo, _Faster than the Speed of Light_. Perseus Publishing, Cambridge, MA. 2003.)
    Suggestions for further lecture notes from Alvaro Véliz:
    Suggestions from Seth Strimas-Mackey:
    • James Binney's (Oxford) video lectures on Quantum Mechanics.
    • Shankar has two video lecture series that I imagine would be excellent (haven't watched them myself):  Series 1 / Series 2.  Both Shankar's and Binney's lectures can be found on iTunes for free.
    • A useful page of lecture notes on several topics in theoretical physics is that of Eric Poisson (U of Guelph).
    • A page with lecture notes for applied mathematics that is helpful (for example, for learning basic calculus of variations at the level good for physics).
    • For Quantum Field Theory, Mike Luke of U Toronto has an excellent page of references (including his own excellent notes, which are basically an abridged version of the famous Sidney Coleman ones). There are also problem sets on this website which are the best way to learn! Mike Luke
    • Finally, possibly the most amazing resource of all is the huge collection of lectures on a wide variety of (fairly advanced) topics in theoretical physics from the PSI program at Perimeter Institute:  Perimeter Scholars
    Suggestion from Daniel MacIsaac:

    Acknowledgements

    The number of people who have helped build, maintain and improve this website is growing rather quickly. I would like to thank and acknowledge them here:
    • Several people have contributed to the website via feedback, responses and questions, etc.: Rob van Linden, Robert Tough, Thuy Nguyen, Tina Witham, Jerry Blair, Jonathan Martin, David Cuthbertson, Trent Strong, Hisham Kotry, John Glasscock, Alvaro Véliz, Seth Strimas-Mackey, Daniel MacIsaac, Adrian Belarr, James Melville, Aditya Thakkar, Niall Devlin, Hossam Halim, Kelly Ann Pawlak and many others.
    • Others have assisted extensively in updating, renewing and finding reliable resources for this website: Aldemar Torres Valderrama, Panos Betzios.
    Please direct any questions, comments or suggestions to Nava Gaddam (gaddam@uu.nl).



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