Can I learn quantum mechanics?
May 30, 2009 9:03 AM   Subscribe

I'm reading Quantum: a Guide for the Perplexed and I'm enjoying the graphics, history and simplification of the math and science used to explain quantum mechanics. But I'm reasonably well versed in math and science - I took a year of college physics, linear algebra, and diff eq about ten years ago. Is there any chance of me learning to understand the equations and papers of Planck and Einstein that are the basis of QM? Are there any good books that could help walk someone like me through this stuff? Or am I stuck as a layperson unless I earn a degree in math or physics?
posted by Grundlebug to Science & Nature (14 answers total) 19 users marked this as a favorite
You could tackle the Feynman undergraduate lectures, which now comes with his Tips on Physics which can help polish up your math.
posted by nicwolff at 9:34 AM on May 30, 2009

You should be able to handle most if as long as you have a good grasp of matrices. I think if you've taken a course on linear algebra/differential equations you should be fine.
posted by voltairemodern at 9:57 AM on May 30, 2009

I'd say that the background in linear algebra (and a bit of PDEs) is really all you need. Honestly, I would reccomend picking up an elementary textbook in QM (Griffiths is a great choice), and working through it. You might be surprised how much you get from it.
posted by vernondalhart at 10:11 AM on May 30, 2009 [1 favorite]

And, on that note, link to the book in question.
posted by vernondalhart at 10:12 AM on May 30, 2009

As noted above, linear algebra and differential equations are really all you need to understand a "real" introductory quantum mechanics textbook. As noted above, Griffiths is an excellent choice; you might also look at Marvin Chester's Primer of Quantum Mechanics, which is an interesting blend of the philosophical and mathematical sides of QM.
posted by Johnny Assay at 10:20 AM on May 30, 2009

As a physics undergrad, the prereqs for the QM for majors class were just linear and diffeq. You should be ok. This book was the one we used. I haven't gone through them in detail, but the Open CourseWare has several intro QM classes.

The Planck papers are an amalgam of things that you wouldn't necessarily think of as QM. The first black-body paper was empirical, the second entropy-based, the third assumes quantized energy, but not because he thought that was really meaningful. All three will rely on understanding E&M quite well, as well as the behavior of oscillators.

Similarly, the 1905 Einstein paper is not that complex if you understand the basics of E&M behavior of an oscillator and something about entropy. It does go through a variety of experiments and evidences which require knowing a bit about the science as it was at the turn of the century.

In summary, if your goal is to understand the Planck and Einstein papers, then you do not really need to know about what we think of today as QM; they didn't. You do need to learn about classic E&M and a touch of statistical mechanics.
posted by a robot made out of meat at 10:29 AM on May 30, 2009

First of all: awesome for you! :-D. (I'm a physics major.)

I'd suggest Griffiths's Introduction to Quantum Mechanics. That's just about the perfect level, and I thought it was a great book for learning, without getting bogged down in stupid calculational shit (ugh, Shankar, I'm looking at you). It goes over pretty much all of the undergrad curriculum.

However, note that textbooks will often gloss over some of the interesting foundational issues in QM. Getting a handle on these is trickier, especially since there are a lot of crackpots out there who like to play with toys they don't understand. (But there's a lot of good research too!) It's more basic than Griffiths, but I found Baggott's The Meaning of Quantum Theory to be a really good introduction to these, and it's significantly beyond the usual popular-science level (even if it doesn't assume that you have undergrad-level knowledge).

Also, I'd like to second a robot made out of meat's point about the early papers not actually being about QM. Proto-QM is kinda annoying to read, in my opinion, but on the other hand lots of others seem to get excited about watching science unfold in a historical sense (instead of wanting to skip to the final results we have these days).
posted by Jacen Solo at 10:57 AM on May 30, 2009

Is there any chance of me learning to understand the equations and papers of Planck and Einstein that are the basis of QM?

the chances of you learning anything by reading planck and einstein and fairly slim to none (for lots of reasons)... on the other hand you have the prerequisites for an introductory course in quantum mechanics. I don't recommend the Feynman lectures, they're insightful but not very pedagogical.

I would recommend something like:

(get the cheap used copy)

however, don't be surprised if you find yourself just as unable to answer 'big questions' even if you can do all the exercises...
posted by geos at 11:19 AM on May 30, 2009

personally, i didn't like griffiths...

the book is small and cheap, but i found griffiths' sense of humour really annoying. if you don't mind spending an extra couple of dollars, get this book. It is longer, i think the math requirement is not as high as with griffiths, and it contains much more information of applications of quantum mechanics inside. it was my text for an intro to quantum class i took a few years ago (the texts for quantum were griffiths and shankhar), and i used it as my primary source for studying quantum for my gre last year.

griffiths will go through some of the math, but in any textbook on quantum, it is easy to get bogged down by thinking of everything as wave functions, rather than as particles or as photons or whatever you are dealing with. i found that eisberg gives a more physical description of qm systems. it discusses wave functions, but unlike griffiths, goes on to describe solid state systems, 2-particle systems, and other interesting and useful stuff. if you want other interesting applications, i always liked chandrasekhar. he's a bit technical, but gives a pretty clear and lucid explanation of statistical mechanics, and gives a good example of how they interact with qm (i.e. white dwarf degenerate stars)... then again, i'm an astronomer at chicago. i may be biased.

good luck!

p.s. i agree with geos. the plank/einstein paper is not the best place to start (neither do i think it is your best goal). texts written almost after almost 100 years of experimenting with qm and contemplating the basics of qm are probably better.
posted by chicago2penn at 1:04 PM on May 30, 2009

You will see lots of recommendations for Griffiths and a few for other books, but next semester, I am instead using this fairly new book by the incredibly talented D. A. B. Miller to teach QM. In my opinion, it's clearer than anything else out there, and it's well-suited for someone with a decent linear algebra background.
posted by JMOZ at 4:09 PM on May 30, 2009 [1 favorite]

You don't mention what kind of diff eq's, though. If you can handle PDEs, you can handle quantum mechanics just fine. Griffiths is the book I used, but I suspect any textbook you like should be fine to get you started. If you just got as far as ODEs, take some time out to learn PDE's first. Brown and Churchill is the book I used. It looks like there is a newer edition now, so this one has some cheap used copies available.
posted by rossmik at 7:42 PM on May 30, 2009

I used to have no good answer to this question. Now I do: Road to Reality, by Roger Penrose.
posted by fatllama at 1:31 AM on May 31, 2009

... or, if you are a freegan: Motion Mountain.
posted by fatllama at 1:31 AM on May 31, 2009

Response by poster: Thanks for all the great suggestions!
posted by Grundlebug at 2:28 PM on May 31, 2009

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