Recommendations for Study Materials [QM]

[xWaffle]

Hello all,

I'm taking my first actual quantum course this semester. I went over "briefly" some quantum mechanics Fall of 2012 in a Modern Physics course during my sophomore year, currently I'm a junior.

To get straight to the point, this course is making me miserable. I had high hopes for this course but they are being killed fast. My main motivation for even studying physics is actually astrophysics, and more and more I hear from my professors that quantum is becoming more and more important in astro specifically.

I am not sure if I am miserable in this course because of lack of math practice, or because of the teacher's style. I feel that I have learned very little actual physical concepts, and everything we do is just so bloated with ridiculous calculus.

For example, right now I'm working on a problem where I am finding <x>, <x^2>, <p>, and <p^2> of a Gaussian wave packet, after having already spent the past 6 hours just finding the probability density to plug into the formulas for those! We've barely even mentioned what wave packets actually are, what the time evolution of this thing actually means, what it is even doing..nothing!

We started off the course opening up with some brief statistical machinery, and then jumped right into math overload. I don't feel like I've learned much physics. The homework assignments are professor-generated problems, so even though "we have a textbook," reading it doesn't much help with the HW problem sets, because the HW problems have nothing to do with what section of the book we should be in.

How do you guys keep motivation for this beast of a topic? What is the best way to approach it?

 

[bhobba]

Mate read the first 3 chapters of Ballentine - Quantum Mechanics - A Modern Development:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

What you are doing now is simply preparation for the real deal in that book. When you read it you probably won't understand it all, but if you keep in mind this is what you are heading towards it hopefully will give you perspective and motivation for, from what you said, is basically math manipulation - not understanding.

If I was giving a course on QM to beginning students it would be a cut down version of Ballentine and based on the following:
http://www.scottaaronson.com/democritus/lec9.html

Both physics and math is about concepts - not long manipulations of dubious value.

Thanks
Bill

 

[llstanfield]

I'm starting from the very bottom of learning physics, and with my personal experience, I've found that mathematics and physics (including astrophysics) have an intricate relationship with each other. However, given your case, I'm not exactly sure why the mathematical understanding of quantum mechanics is necessary to learn more about astrophysics ( given the two are different in my opinion).

This is all conjecture on my part. Perhaps it's necessary to learn about the quantum math as it relates to light in your field, because learning about galaxies is learning about light. On the other hand, based on my understanding, most astrophysicists today can simply plug in equations/calculations into a computer to find a particular answer they are looking for. But, being a private physics student as myself, I'd say utilize the internet or other external resources to help on your journey. The motivation follows behind the yearning to understand what it is you're trying to find out more about.

 

[Mordred]

As one that has learned cosmology and astrophysics myself without formal training, I can only wish I had a calculus course as well as a good understanding of quantum mechanics.

Here is a quick list of where an understanding of quantum mechanics and QFT which can be described as ( relativistic quantum mechanics) would come in handy.

1) false vacuum Allen Guth
2) Hawking Berkenstein radiation
3) Parker radiation
4) loop quantum gravity
5) statistical distributions and diffusion of a perfect fluid

not to mention understanding all the various forms of fields in this article.

Fields
http://arxiv.org/abs/hepth/9912205

all of which applies to cosmology in some fashion even if it isn't at first obvious. For example how do you understand the high energy particle physics involved in the universes first moments?

on the purely astrophysical side try understanding all the processes described in this article

Foundations of Black Hole Accretion Disk Theory
http://arxiv.org/abs/1104.5499

trust me the math background will make it far easier for you to go further in astrophysics than you possibly could without it.

 

[vanhees71]

Well, to understand any physics there's nothing more important than quantum mechanics. I don't know, what you can do in astrophysics without quantum theory. It depends a bit, what kind of astrophysics you want to do, but to understand how a star is shining you need a lot of quantum theory and nuclear physics.

The problem with quantum theory is not so much the math. It's pretty easy: You need some basic understanding of linear algebra and Hilbert spaces, the solution of partial differential equations (particularly the Schroedinger equation) and some basic understanding of what probabilities are.

The true challenge is to understand the physics behind quantum theory, particularly the meaning of observables and states in a probalistic indeterministic theory. Although Ballentine is a great book, which gives right away the minimal statistical interpretation which is the least esoteric and working interpretation of every physicist in the lab as well as a solid foundation of the theory based on symmetry principles, it's not a good book to begin with, because there you get also already in the beginning into quite formal mathematical things like the rigged Hilbert space. Also this is the right modern mathematical language to understand quantum theory on a deeper level (particularly the meaning of essentially self-adjoint operators and their domain of definition; continuous spectra of those operators, etc.), this is also not helping the beginner to understand the physics behind quantum theory.

A good compromise between mathematical rigor and physical intuition is

J. J. Sakurai, Modern Quantum Mechanics, Addison-Wesley

It starts with the Stern-Gerlach experiment and explains the physics right away in the bra-ket formalism. This provides the fundamental understanding behind the Hilbert-space formalism in the utmost simple case of a finite-dimensional Hilbert space of spin 1/2, which you have to master anyway at some point since electrons, protons, and neutrons are spin-1/2 particles forming the basis of atomic and molecular physics. Then the book goes on with the Dirac algebra of position and momentum, the Schroedinger equation, the hydrogen atom etc. Also the chapter about scattering theory is very good. Another good thing is that it also introduces to the path-integral formalism and some interesting things like the Aharonov-Bohm effect, etc. After studying this book, you can begin to read Ballentine and other more advanced books, among them also Weinberg's newest textbook:

S. Weinberg, Lectures on Quantum Mechanics

 

[WannabeNewton]

How do you guys keep motivation for this beast of a topic? What is the best way to approach it?

When learning a new physical theory I always find it easiest to first do a masochistic amount of problem sets in order to get a handle on the various calculational aspects of the theory and only then move on to an attempt at understanding the foundational concepts, especially when it comes to QM. I presume your class is using Griffiths?

By the way you shouldn't expect the same ubiquity of "physics" in QM at the introductory level that you're used to in EM, classical mechanics, waves/oscillations, and possibly relativity. You'll notice that a lot of the problem sets in many QM books (introductory and even advanced) tend to be very mathematical (but not in the fun sense), very algebraic, and little in the way of truly mind-wracking physical concepts which is the opposite of (rigorous) introductory books on classical mechanics and EM e.g. Kleppner/Kolenkow and Purcell respectively. In Griffiths you'll find a lot of these absolutely trivial but annoyingly tedious problems such as calculations of expectation values of observables for infinite square wells and harmonic oscillators and whatnot whereas in for example Kleppner you'll find beautiful problems that involve very little tedious computation but require a fair amount of physical ingenuity like in the famous problem of a ball elastically bouncing back and forth between moving walls. Just like you I would much prefer the latter but at this stage you're stuck with the former.

 

[xWaffle]

When learning a new physical theory I always find it easiest to first do a masochistic amount of problem sets in order to get a handle on the various calculational aspects of the theory and only then move on to an attempt at understanding the foundational concepts, especially when it comes to QM. I presume your class is using Griffiths?

By the way you shouldn't expect the same ubiquity of "physics" in QM at the introductory level that you're used to in EM, classical mechanics, waves/oscillations, and possibly relativity. You'll notice that a lot of the problem sets in many QM books (introductory and even advanced) tend to be very mathematical (but not in the fun sense), very algebraic, and little in the way of truly mind-wracking physical concepts which is the opposite of (rigorous) introductory books on classical mechanics and EM e.g. Kleppner/Kolenkow and Purcell respectively. In Griffiths you'll find a lot of these absolutely trivial but annoyingly tedious problems such as calculations of expectation values of observables for infinite square wells and harmonic oscillators and whatnot whereas in for example Kleppner you'll find beautiful problems that involve very little tedious computation but require a fair amount of physical ingenuity like in the famous problem of a ball elastically bouncing back and forth between moving walls. Just like you I would much prefer the latter but at this stage you're stuck with the former.

You guessed it, we're using Griffith's. If you can call it "using."

We aren't assigned reading, we aren't assigned problems out of the book. 99% of the time when that happens in a class, you think to yourself, "why do I even need this book, then?"

I have purchased all of the books for all of my physics courses so far, and I plan on keeping them. Because I do read them. One of my best professors told me he has kept all of his books, and can still use them as relevant reference material to this day. Usually, however, our homework comes from textbooks and we are also assigned reading (so that we have some semblance of what's being talked about in lecture beforehand). My E&M class currently uses Griffith's E&M book this way.

With that being said, I did read the first two chapters of Griffith's QM, but I haven't done any of his problems. First midterm coming up next Tuesday for Quantum. I'll definitely be plowing through the Griffith's problems this weekend (seems to be my best bet at the moment).

Thanks for everyone's responses so far, keep them coming if anyone else has anything to add!

 

[bhobba]

You guessed it, we're using Griffith's. If you can call it "using."

Believe it or not Griffith's is actually a good book - just a bit pricey. But some lecturers don't seem to worry too much about the cost to their poor long suffering students.

Its an intermediate level book being the bridge to the better, but more advanced, books like Ballentine. Books at that level can take a number of routes each with pro's and cons. Griffiths takes the showing you how to solve problems route, but leaves exactly what's going on often up in that air. For example, it doesn't explain the true basis of Schrodengers equation, the momentum operator etc is symmetry (if that intrigues you, and it should, see chapter 3 of Ballentine). It gives some hand-wavey justification based on a vague understanding of De-Broglie matter waves, wave particle duality and what not. If you are a THINKING student it would, and should, leave you cold. It did for me when I read books at that level - it raised more questions than answers for me.

I agree entirely with Vanhees. But since you are taking the course all you can really do is persevere. I don't have Sakurai but its reputation is excellent, and I would have that as supplemental reading to Griffiths.

Vanhees is correct - Ballentine is more advanced than is good for a beginning student. But I still do suggest you read the first 3 chapters - that way you will see how the hand-wavey stuff of Griffth is fixed as well as a proper axiomatic development based on just 2 axioms - that's right QM is really just two axioms. You probably won't understand all the math but will get the gist and hopefully realize questions in the back of your mind from Griffiths do have an answer and what you are doing now is simply a bridge to the better treatments.

Thanks
Bill

 

[jtbell]

Another book you might consider as a complement to Griffiths, that might give you some practical help with your homework, is this one:

https://www.amazon.com/dp/0137479085/?tag=pfamazon01-20

(Yikes, it's expensive now, but maybe your library has a copy you can borrow.)

It goes into more detail than any other book I've seen, on techniques for hacking through the calculus and algebra needed to solve problems like the Gaussian wave packet and barrier penetration ("tunneling"). Because of that, it's more than twice as thick as Griffiths.

 

[ahsanxr]

If you want a good discussion of the physics AND math behind QM, start reading Shankar. Now. He starts off with a very nice chapter on the relevant mathematics, followed by a chapters on classical mechanics and the experimental basis of QM. Chapter 4 is then a very enlightening read, since he carefully goes through the postulates of quantum mechanics, and discusses each one in detail. From then on, he does the standard topics, which can then be found in Griffiths as well, which skips all of the things Shankar says and just jumps straight into "alright, let's start solving Schrodinger's equation!". But I would say, if you're really looking at someone to carefully explain the physics and motivation behind QM, and how it differs from traditional physics and why you have to spend so much time calculating these god damn expectation values, then there's no better place than Shankar, at least for a beginner.

Believe me, there is much more to QM than working in position space and doing tedious algebra calculating expectation values for nasty wave functions. But you won't find that in Griffiths. I blame him and his book for the terrible way QM is taught to undergraduates these days.

Oh and if you want help with solving problems, there's this great book by Zettili. It also has a fairly good discussion of the general aspects of QM, but the real gem that the book offers is that at the end of every chapter, there are 10-20 explicitly worked out problems.