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I'm an aspiring physicist who wants to self study some Quantum Physics. My thirst for knowledge is unquenchable and I can not wait 2 more years until I get my first quantum physics class in university, so I want to start with a self study. I am enrolled in a grammar school and the most gifted among the gifted (not my description, mind you, I hate coming off as cocky, sorry) are enrolled in a special 'project'. We are allowed to take 3 school hours a week off in order to work on a project, which can be about anything you want, from music to mathematics. On the 4th of April we have to present our projects. Last year an acquaintance of mine did it about university level mathematics, so I thought, why not do it about university level physics? It is now the 3rd of October so I have half a year. My question is, where can I conduct a self study of quantum physics? Starting from scratch? And is it possible for me to be able to use and understand the Schrödinger equation by April? What are good books, sites, etc. that can help me? My goal is to have a working knowledge of BASIC quantum physics and I would like to understand and be able to use the Schrödinger equation. Is this possible? What is needed for these goals?

Qmechanic
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kamal
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  • Do you have any experience with linear algebra, calculus or differential equations? – DJBunk Oct 03 '12 at 15:58
  • None with linear algebra, but I do with calculus. – kamal Oct 03 '12 at 16:03
  • I would say it depends on how ambitious you are in general learning a subject, but I really doubt 3 hours a week will do it. With some effort you might be able to learn some neat qualitative things, but I highly doubt you will be solving the Schrodinger eqn etc by April. I suggest doing something more specific like learning about things like the double slit experiment and the photoelectric effect. Those types of things you can start with Wikipedia to see if it interests. Don't let me discourage you though! – DJBunk Oct 03 '12 at 16:14
  • Related: http://physics.stackexchange.com/q/33215/2451 and http://physics.stackexchange.com/q/38735/2451 – Qmechanic Oct 03 '12 at 16:15
  • Of course those 3 hours a week are only during school time, I expect to spend around ~10 hours a week for this, some weeks more and some less, but at least 10 hours, that I know. I already have a working knowledge of the double slit experiment and photoelectric effect, so I think I am ready for the next step (although I am not certain what that might be). – kamal Oct 03 '12 at 16:17
  • Also, I have 2 big books on linear algebra lying around at home (my father's I believe) so would you recommend me to do some studying of that? – kamal Oct 03 '12 at 16:19
  • Either of Ron's books are fine, also Griffith's' Intro to Quantum Mechanics' Standard. I just want to clarify from before - if you are just interested in QM want to put some time in, then totally go for it. My only concern is that it sounds like you have to have something to show for you work and Im concerned how this could come together in a project for you in that time span. – DJBunk Oct 03 '12 at 17:05
  • You can watch videos from here and lectures from here (first two atleast). – swish Oct 03 '12 at 16:41

3 Answers3

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Just pick up Dirac's book "The Principles of Quantum Mechanics" and read it in conjunction with "The Feynman Lectures on Physics Vol III". Don't waste time with linear algebra, the entire content of the undergraduate courses can be learned in half a day. Don't worry about the infinite dimensional nature of the thing, just reduce all the spaces to finite dimensions.

Also, be aware that "gifted" is a political label that has nothing to do with you, it's just a way for schools to segregate students by their future social class. It's not the analog of special needs, because the students in gifted classes are no different from the students in usual classes, except that they are given a slightly better education. Don't be fooled by a label into thinking you are somehow special, everyone is ordinary, including Einstein and Dirac. One has to do good work despite this, and those folks show it is possible by assiduous effort.

Ron Maimon
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    Trouble is you're seeing things from the way you did things, and not how they can be done today using what's available. Have you seen Susskind's QM video lectures for example? Don't you think watching videos while taking notes is more productive? I'm with you and Howard Gardner on "giftedness" – Larry Harson Oct 04 '12 at 02:13
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    @LarryHarson： I agree that I'm out of date, but it cannot be overemphasized how important it is to read the classics. Dirac's book is timeless, it is lucid, it is brief, it starts with first principles, and its mathematics is self contained. It's path of development is unique and very illuminating, being independent of both Schrodinger and Bohr. Susskind's videos I am sure are excellent, but I have a soft spot for Dirac, who was one of my closest friends throughout adolescence. As for giftedness, it is worst for the "gifted", who are made cocky and incapable of the humility required for study – Ron Maimon Oct 04 '12 at 03:04
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    I wonder how you think that ''Don't worry about the infinite dimensional nature of the thing, just reduce all the spaces to finite dimensions.'' can be done without some understanding of linear algebra.... – Arnold Neumaier Oct 04 '12 at 15:05
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    @ArnoldNeumaier: Because I didn't study linear algebra and I read Dirac and had no trouble. – Ron Maimon Oct 04 '12 at 16:09
  • I haven't read Dirac, but then he must introduce along the way the linear algebra needed along the way.... – Arnold Neumaier Oct 04 '12 at 18:22
  • @ArnoldNeumaier: He does--- but it's not about row reductions and determinants, but eignevalues and eigenvectors in Dirac's notation, and this is straightforward. The notation also takes care of spaces and dual spaces, and basis expansion, and the only thing you need to complete it is the axiomatic formulation of vector spaces, which can be learned in half a day once you understand the practical Dirac tools. This is the easiest path for self-study, at least in my experience, although from skimming linear algebra books, you pick up a useful technique or two. – Ron Maimon Oct 04 '12 at 18:37
  • I have almost finished a first year college course of Linear Algebra, so it's up to scratch, I won't need to worry about it no more. – kamal Oct 27 '12 at 12:11
  • @RonMaimon I also don't care for the 'gifted' label, it just enables me to take 3 hours a week off from useless classes like Latin and Classical History to work on things I deem more useful. – kamal Oct 27 '12 at 12:14
  • @kamal: One mathematical thing you can learn using Latin and classical history (these are former high-class markers, now it's "gifted") is that you can use these to understand the history of recursion in linguistics, something of current research interest. Latin uses both pronouns and cases to do recursion (the cases go away in Fr/Sp/It). This shows the Romans are still adapting to the newfangled recursive grammar. The Christianization of the Roman Empire is also an example of Marx's "class struggle", with Christianity playing the role later taken by Marxism, a topic censored in schools. – Ron Maimon Oct 27 '12 at 12:23
  • That may very well be true, but don't overestimate the high school curriculum. 'Latin' just mean translating boring texts from writers such as Tacitus (who doesn't appeal to me, with his sine ira et studio, what a joke) and Classical History is just about the Greek/Roman Pantheon and some other boring stuff. Complete waste of time if you ask me. – kamal Oct 27 '12 at 12:33
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    @kamal: Yes, it's a waste of time, but it was always a waste of time, it was a high-class marker to know Latin (you must be living in some former European colony to have such an education, class-markers were very important under colonialism). High-class markers (King's English, Queen's accent, a Rolex, high-status position) are always extremely time-consuming to acquire (or else they wouldn't work to mark high-classes), and this is why science is always done by low-class people who hate Latin and dress like slobs. The ancient stuff can be useful for Marlowe/Shakespeare, that's about all. – Ron Maimon Oct 27 '12 at 12:43
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Without having understood matrices and their interpretation as linear mappings (operators) it is very difficult to get a reasonable understanding of quantum mechanics. So you should spend some time on elementary linear algebra. Wikipedia is not bad on this, so you could pick up most from there. (To start with. For basic math, Wikipedia is almost completely reliable, which is not the case for more specialized topics. In case of doubt, cross check with other sources.)

Today, the shortest road to quantum mechanics is probably quantum information theory. For online introductory lecture notes see, e.g.,
http://www.qi.damtp.cam.ac.uk/node/223
The following lecture notes start from scratch (use Wikipedia for the math not explained there):
http://www.itp.phys.ethz.ch/education/lectures_fs09/QIT/script_05.08.2009.pdf
This one might also be useful:
http://michaelnielsen.org/blog/introductory-lecture-notes-on-quantum-information-and-computation/

In quantum information theory, all Hilbert spaces are finite-dimensional, wave functions are just complex vectors, and the Schroedinger equation is just a linear differential equation with constant coefficients. So you also need to learn a little bit about ordinary differential equations and how linear systems behave. Again, this can be picked up from Wikipedia.

In more traditional quantum mechanics, the Schroedinger equation is a partial differential equations, and wave functions are complex function depending on one or more position coordiates. On this level, you need to understand what partial derivatives are and have some knowledge about Fourier transforms. Again, this can be picked up from Wikipedia. Then you might start with
http://arxiv.org/abs/1201.4234

You may also wish to try my online book http://lanl.arxiv.org/abs/0810.1019
It assumes some familiarity with linear algebra and of partial derivatives, but little else. Some basic questions are also answered in my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html

Community
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Arnold Neumaier
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  • +1 these are nice sources if you get stuck on linear algebra, but I never got stuck on the linear algebra, rather the sticking points were the partial differential equations and the path integral. – Ron Maimon Oct 04 '12 at 18:17
  • @RonMaimon: kamal doesn't want to understand the path integral by April. And one needs very little from PDE as long as one doesn't want to solve numerically a real problem. Thus if he has no trouble with the linear algebra and with Fourier transforms, he'll have no trouble at all! – Arnold Neumaier Oct 04 '12 at 18:20
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    He should be more ambitious then--- the speed with which one can self study has increased tenfold in the last decade. – Ron Maimon Oct 04 '12 at 18:21
  • @RonMaimon What would you suggest being good for me to set as a goal? You seem like a very informed man and I would like to ask for your personal advice. Of course I am also busy with sports, and I'm starting to learn LaTeX, so I'd say I spend 10 hours a week on this. – kamal Oct 27 '12 at 12:18
  • @kamal: The only goal is to understand what has been done and push it forward, like everyone else tries to do. For this, you can follow a sequence more or less like Dirac/Feynman/Onsager/Landau/Gell-Mann/Anderson/Mandelstam/Polyakov/Parisi/'tHooft/Scherk/Schwarz/Susskind/Witten (with about two dozen more authors I left out, sorry). I gave a simple but flashy thing which can be tackled after understanding basic QM here: http://physics.stackexchange.com/questions/41780/quantum-phyics-project-for-a-high-schooler/41804#41804 (your question). Maybe read Nielson and Chuang, learn complexity classes. – Ron Maimon Oct 27 '12 at 12:31
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If you want to understand quantum physics, you have to understand Fourier series and Fourier transforms. The best introductory text ever, is the book Who Is Fourier?. Do not be fooled by its cartoonish appearance, this is a serious book as can be demonstrated by the fact that the name on the top of the list of advisers is Yoichiro Nambu who is the 2008 Nobel prize co-winner:

"for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature."

Then I would work to gain an understanding of the Heat Equation. The Schrodinger equation can be described as the quantum version of the heat equation (except, what is diffusing is probability).

Fourier developed the Fourier series in order to solve the question of how heat diffuses in a material. If you understand these things, you can understand quantum mechanics within a few months.

Freedom
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    For fourier analysis, Koerner is a great source, with both accurate historical material and fascinating applications, including primes in arithmetic progression and an alternate RW proof of Picard's theorem: http://www.amazon.com/Fourier-Analysis-T-246-rner/dp/0521389917. I didn't read the cartoon book, but I doubt it has the same depth as Koerner, which is one of the great pedagogical mathematics books, along with Davenport's number theory. These were thankfully used by the mathematics professors I had as an undergraduate, and they were very good folks. – Ron Maimon Oct 04 '12 at 18:19
  • @RonMaimon Thanks, I will see if I can pick up a copy, it looks pretty cool from the excerpts on amazon – Freedom Oct 04 '12 at 18:30
  • @Hal Swyers thank you for giving insight into importance of heat equation in understanding the Schrodinger equation. I wish I could get free e-copy of this book "who is fourier" else i will try buying it. – baalkikhaal Oct 27 '12 at 10:33