Best Quantum Mechanics Texts for Graduate Students | Expert Recommendations

[tornpie]

I'm a mathematics grad student looking to take graduate quantum mechanics in the fall. The prof isn't using a text, but I think I might want to have one around in case. Are there any Quantum Mechanics texts that are like a Rudin is to Analysis?

 

[tornpie]

One other thing, I haven't taken any physics since calculus based introductory physics, like Halliday, Resnick.

Also, are there texts like this for the other core areas of physics like Grad E+M, Grad Mechanics, and Grad Thermodynamics?

 

[robphy]

Check out http://www.ocf.berkeley.edu/~abhishek/chicphys.htm
(Scroll down... this links should point to lower portions of the page... but the links have a typo in them.)

 

[Galileo]

My class used Griffith's introduction to Quantum Mechanics. The book may be
nice for use in class because of the problems, but for self-study it sucks.

I highly recommend Cohen Tannoudji's "Quantum Mechanics".
The text is clear, elaborate and pedagogically written.

 

[ZapperZ]

So am I the only one here who is ... er... "amused" by the fact that this person is going to be enrolling in a GRADUATE level QM class with only intro physics background? I mean, think about it. Would someone who has completed a year's worth of classes using Halliday and Resnick, be able to comprehend the material coming out of, let's say, Sakurai's "Modern Quantum Mechanics" or even Merzbacher's "Quantum Mechanics" (both of which are typical graduate level texts)? Merzbacher, for instance, doesn't bother much with a single harmonic oscillator (he assumes you have already seen that in undergrad QM), he goes quickly to DOUBLE harmonic oscillator! He also doesn't waste time with simple square well potential in tunneling problems (again, something that one should already know in undergrad QM), he goes quickly into WKB approximation!

Don't get me wrong, I'm not criticizing. If you can do it, hey, more power to you. Maybe I'm just jealous because I am not smart enough and had to go through all the steps in between to get to that stage! :)

Zz.

 

[Nenad]

well, he is a math grad, so he should have a good background on the mathematics. Good luck man.

 

[JohnDubYa]

He is going to need all the luck he can get. QM is more than just applied mathematics.

 

[JohnDubYa]

This thread reminds me of a hotshot electrical engineering student we had in Classical Electrodynamics. On his first exam, he scored THREE out of 100. When the professor placed our graded exams out by his doorstep, he made sure to place the engineering student's on the top.

We felt bad for him, so we stuck it in the middle of the pack. Two hours later, it was back on the top of the stack. Obviously the professor was sending a message.

 

[quantumdude]

I love Sakurai's Modern Quantum Mechanics. It's interesting to read, the exercises are instructive, and it provides a smooth transition to QFT.

 

[Njorl]

My class used Griffith's introduction to Quantum Mechanics. The book may be
nice for use in class because of the problems, but for self-study it sucks.

I highly recommend Cohen Tannoudji's "Quantum Mechanics".
The text is clear, elaborate and pedagogically written.

I liked Cohen-Tannoudji as well.

I agree with JohnDubya. More than any other physics course, I think QM is not just applied math. The actual math involved is some of the easiest you'll encounter in graduate physics, but the concepts are some of the hardest.

Njorl

 

[Njorl]

So am I the only one here who is ... er... "amused" by the fact that this person is going to be enrolling in a GRADUATE level QM class with only intro physics background? I mean, think about it. Would someone who has completed a year's worth of classes using Halliday and Resnick, be able to comprehend the material coming out of, let's say, Sakurai's "Modern Quantum Mechanics" or even Merzbacher's "Quantum Mechanics" (both of which are typical graduate level texts)? Merzbacher, for instance, doesn't bother much with a single harmonic oscillator (he assumes you have already seen that in undergrad QM), he goes quickly to DOUBLE harmonic oscillator! He also doesn't waste time with simple square well potential in tunneling problems (again, something that one should already know in undergrad QM), he goes quickly into WKB approximation!

Don't get me wrong, I'm not criticizing. If you can do it, hey, more power to you. Maybe I'm just jealous because I am not smart enough and had to go through all the steps in between to get to that stage! :)

Zz.

My undergrad EM fields proffessor earned his BA in music, his masters in biology, then "on a whim", thought "getting a PhD in physics would be fun". I wanted to hit him.

I remember undergrad quantum. We got into it like you'd get into a tub full of ice water. It seemed one by one we each had our own epiphanies as we "got it". I can't see plowing through it without this indoctrination, like we did in grad school.

Njorl

 

[gravenewworld]

I used Alberty and Silbey's Physical Chemistry for my undergrad P Chem course. Don't be fooled though, PHYSICAL Chemistry is all about the physics behind Chemistry. This book was very hard to follow, it could easily be, and probably should have been, used in a grad course. Half of the book is dedicated to a very indepth treatment of thermodynamics. The beginning of the second half is for QM and applications of QM such as spectroscopy etc. I'm sure there are physics text on QM that go into more detail into QM, but with this book you can kill 2 birds with 1 stone, thermo and QM. This book provides a very rigorous explanation for thermo and basics of QM.

 

[Njorl]

I used Alberty and Silbey's Physical Chemistry for my undergrad P Chem course. Don't be fooled though, PHYSICAL Chemistry is all about the physics behind Chemistry. This book was very hard to follow, it could easily be, and probably should have been, used in a grad course. Half of the book is dedicated to a very indepth treatment of thermodynamics. The beginning of the second half is for QM and applications of QM such as spectroscopy etc. I'm sure there are physics text on QM that go into more detail into QM, but with this book you can kill 2 birds with 1 stone, thermo and QM. This book provides a very rigorous explanation for thermo and basics of QM.

Interesting. I noticed that most curricula present thermo first, then quantum. This just seems all wrong to me. I remember the first time I studied thermo, it was very unintuitive. I didn't really grasp what I was learning. Actually, I was learning how to solve problems, but not learning any physics. It wasn't until grad school that I learned the quantum foundations of thermo (stat mech really).

It is ironic that this sort of parallels the life (and death) of Boltzmann. Had he developed his theories on the behavior of gases after quantum mechanics became accepted, he might not have had such a terrible time of it.

Njorl

 

[tornpie]

I guess I feel after Rudin, you've pretty much established yourself as a scholar. I've come into contact with all kinds of stuff that comes from quantum in stochastic processes, mathematical finance, functional analysis, etc. I figure the math won't be hard at all leaving me to concentrate on the rest of the stuff.

I'm also wondering if the way to go for the good physics is to skip physics undergrad and concentrate on the math. Physics undergrad courses from my indirect contact (friends taking the classes, etc.) always seemed to be too informal and boring and Gawd do I hate lab.

 

[tornpie]

I'm also leaning towards Landau's book. Sakarai seems a little expensive and extravagant.

 

[Lonewolf]

One other thing, I haven't taken any physics since calculus based introductory physics, like Halliday, Resnick.

Also, are there texts like this for the other core areas of physics like Grad E+M, Grad Mechanics, and Grad Thermodynamics?

Jackson's 'Classical Electrodynamics' and Goldstein's 'Classical Mechanics' are pretty much standard graduate texts for the first two subjects. I imagine you'll have no problems with the mathematics.

I think you should at least become familiar with some standard results from the undergraduate physics courses before diving into the graduate stuff. You'll thank yourself for it later.

 

[marlon]

USE BRANSDEN AND JOACHAIN

THEY ROCK YOUR QM-WORLD

from
marlon brando

 

[vanesch]

I'm also wondering if the way to go for the good physics is to skip physics undergrad and concentrate on the math. Physics undergrad courses from my indirect contact (friends taking the classes, etc.) always seemed to be too informal and boring and Gawd do I hate lab.

All carreer paths are imaginable, but aren't you affraid of learning to fly before knowing how to walk ? I think there is undergrad material you should know. Of course you shouldn't follow the typical undergrad courses, which are meant also to get you to some maturity (which you have acquired elsewhere). But there is simple stuff you should know by heart.

Also, a future physicist who says that he hates experimental work is probably like a medical doctor who hates sick people :-)

cheers,
Patrick.

 

[ZapperZ]

Jackson's 'Classical Electrodynamics' and Goldstein's 'Classical Mechanics' are pretty much standard graduate texts for the first two subjects. I imagine you'll have no problems with the mathematics.

I think you should at least become familiar with some standard results from the undergraduate physics courses before diving into the graduate stuff. You'll thank yourself for it later.

As a case in point, Jackson's book covers the whole undergraduate electrostatic material not just in one chapter, but in the INTRODUCTION of the book, for heavens sake! He fully expects that you already know your undergraduate material by the time you start this book. If you don't, you should stick a fork in you, because you're done!

Zz.

 

[JohnDubYa]

Agreed. Bransden and Joachim rocks! But tough to find when I was in grad school. Has it come back into print?

 

[Lonewolf]

As a case in point, Jackson's book covers the whole undergraduate electrostatic material not just in one chapter, but in the INTRODUCTION of the book, for heavens sake! He fully expects that you already know your undergraduate material by the time you start this book. If you don't, you should stick a fork in you, because you're done!

Zz.

Good point. Even those who have had a full education in undergraduate physics can struggle with EM at the level of Jackson. Pretty, it ain't.

 

[tavi_boada]

landau's books are the paradigm of extravagance and sofistication. in my opinion, sakurai's first 4 or 5 chapters are absolutely brilliant, beautiful and comprehensive.

i would recommend you review your notes on optics and electromagnetism. one of the things that i like the most about sakurai's book is that it starts out shocking you with the stern-gerlach experiment, and you have to know a bit of physics to be shocked (not much though).

in my opinion, there is no bible of quantum mechanics as there is with EM (jackson) and classical mechanics (goldstein). The first chapters of any of the following will do for you: sakurai, bransden,feynman (whole 3rd vol). o recommend you stick to these before venturing with landau.

i must say i don't like the tone of some of the earlier posts. I think physicists are a bit snobbish sometimes. in my opinion this it's great taking subjects that aren't of one's own discipline.

 

[oreopoj]

Shankar forever

Dear friend,
If you're trying to learn quantum mechanics through self-study, Shankar's "Principles of Quantum Mechanics" is the ultimate book.
I know ahead of time that others in this forum will critisize this suggestion, but believe me, if you really want to understand QM, use this book. This first chapter of the book is dedicated to teaching/reviewing the necassary math for QM; this would go well with your background.

 

[tornpie]

I agree with you on the snobbish side, but I get to feeling that way sometimes too in math. Some physics majors decided they wanted to try some topology. The class had the typical 4 or 5 math majors who I knew would be there, and about 15 physics majors. Needless to say, after the first week there was only one lone physics major and he stayed for the duration to his credit.

I think the whole thing has to do with formalism. Seems to me that QM was developed with mathematical formalism instead of guys in the 20's smoking up and throwing absurd ideas around. True that some of it was due to experimentation, but the true meat of the subject was math.

I try to tell anyone in physics (or any subject), that you'll never be worse off after taking a math class, especially pure math. Any monkey can throw numbers into an equation, but to truly understand what the hell is going on there is invaluable. The physics people should spend some more time proving numbers irrational and delta-epsilon arguments.

Personally, I see little difference between physics and math.

 

[ZapperZ]

Considering that *I* was the first one on this string to throw out the cold water on this whole thing (and thus, probably one of the "snobbish" one), let me just point out that both of you did NOT even address the validity of the points that I made via the examples I gave. Where was my assertion of the assumed prerequisites for a graduate level QM class wrong? Was I completely baseless at being "amused" at the skipping of entire knowledge of undergraduate QM (and classical mechanics and classical E&M, which do, after all, come into play in QM)?

And this has nothing to do with taking "other" classes outside of one's major. Why would I want to discourage people from taking physics classes, considering that this would add to more money going to physics departments? All I wanted to do was to leave the impression that, for us mere mortals, jumping into a graduate level QM (or E&M, or Classical Mechanics) without adequate preparation isn't something usually recommended.

So how was that being "snobbish"?

Zz.

 

[tornpie]

Sorry ZapperZ.

I guess there is some amusement to be had at skipping the entire undergrad sequence of physics. As far as the prerequisites, you are probably right too. But it seems like in physics and math, the courses tend to be self-contained since they are redoing everything in a rigorous manner. I'd agree with you more for a Eng. Lit., Poly Sci, (insert your favorite humanity to bash here) to jump into grad level physics and math.

 

[ZapperZ]

Sorry ZapperZ.

I guess there is some amusement to be had at skipping the entire undergrad sequence of physics. As far as the prerequisites, you are probably right too. But it seems like in physics and math, the courses tend to be self-contained since they are redoing everything in a rigorous manner. I'd agree with you more for a Eng. Lit., Poly Sci, (insert your favorite humanity to bash here) to jump into grad level physics and math.

I don't quite understand you.

When I was an undergraduate student, I took various "advanced level" classes in Litrature, Environmental Studies, Philosophy, etc as part of my liberal arts electives. However, I doubt that one could even jump in a 200 level physics classes without adequate preparations! I can see this clearly in that I never encounter an English Lit major, for example, taking an intro to Modern Physics class to fulfill his/her physical science elective. Don't believe me? Try giving one of them a copy of, let's say, Tippler's modern physics text and see how long for them to decipher just the first chapter alone.

I also do not understand what it means for a physics course to be "self-contained". For example, in Liboff QM text, was there any clear explanation on what exactly is meant by "orthornormal" functions? I hate to think that a student trying to understand the non-intuitive nature of QM is also forced to also forced to study the mathematics at the same time. This is the least desirable way to learn any physics when the mathematics gets in the way. So I highly disagree that these courses are "self-contained".

More than anything, practically all physics courses require that you have the "skill" to be able to analyze and decipher a given problem. The ability to look at a problem, to know what kind of "frame" or coordinates to use, to be able to think 2 or 3 steps ahead in setting up the problem, and the ability to quickly realize when things just simply do not look right, are all analytical SKILLS that one simply cannot learn by just reading a book - they can only be ACQUIRED through repeated exercises and practice!

To use mathematics effectively in applications, you need not just knowledge, but skill. Skill can be obtained only through practice. You can obtain a certain superficial knowledge of mathematics by listening to lectures, but you cannot obtain skill this way.

--- Mary Boas in "Mathematical Methods in the Physical Sciences, 2nd Ed. (Wiley 1983)

Zz.

 

[kakarukeys]

the maths in qm are mainly Linear Algebra (Complex inner product space), Differential equations, Continuous Groups...

If you want to learn the maths in QM, all the books that were recommended are not suitable. there is a series of Physics books written for Mathematicians, I forgot the names, but all books have yellow covers.

If you want to learn Physics mixed with a lot of maths. Maybe P.A.M. Dirac or
Ballentine

 

[vanesch]

I guess there is some amusement to be had at skipping the entire undergrad sequence of physics. As far as the prerequisites, you are probably right too. But it seems like in physics and math, the courses tend to be self-contained since they are redoing everything in a rigorous manner.

Just for information, I also changed fields: I first did a master in electromechanical engineering, and then I directly did my masters in physics. Even though there is probably more coverage between engineering and physics than between math and physics, you have to get used to "a different culture" and people from within the field (my physics co students) would have liked to see me fall on my face, I'm sure. That didn't happen at all, but I do have to say I had to take up quite a lot of "undergraduate" material on my own. However, other things turned out to be much easier for me than for my fellow students, so this compensated.

Probably the same will happen to you: your co-students will struggle with mathematical ideas you know and find easy, and you will struggle with some physical intuition and knowledge that will seem evident for your co students. So you'll have to work on that on your own, but you will gain time on the more mathematical stuff, so you should be able to handle the thing. However, do not make the mistake of thinking that physics is simply applied mathematics, it isn't. You do not write down the axioms in the beginning and then "turn the crank" ; there is always some extra physical input.
I don't think you can get around skipping undergrad physics ; only you'll probably be able to digest it in a much faster pace than by following undergrad courses. But somehow you'll have to get through it.

cheers,
Patrick.

 

[tornpie]

Here's the email I've been getting back from the profs for QM:

It is assumed that you know differential equations and matrix theory. Some knowledge of infinite dimensional spaces--Hilbert spaces is also helpful. The math demands are not all that high. I am around if you want to discuss this more.

Concerning the text:

The course is mainly based on lecture notes that I post on courseweb and other resources. I ordered copies of Messiah as a good purchase at $29 but it's not really the course textbook.

and classical mechanics:

If you have taken any undergraduate course on mechanics that is most of what you need. If you already have the math background then you should be in pretty good shape. The course will be self-contained and I will give a brief reminder of the main aspects of particle mechanics. Mainly what you need to know are: linear and angular momentum for particles, conservation of momentum and energy, potential and kinetic energies and equations of motion for particles. all of that is contained in any undergrad course.


BTW, I was curiuos, what kind of math courses have you taken Zapper? Seems like a background in linear algebra and analysis would come in handy for you. Particularly, the material covered in Spivak, Lax, and Rudin.