Best Quantum Mechanics Texts for Graduate Students | Expert Recommendations

[Lonewolf]

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.

I found Messiah horrible to learn from, but it makes a great reference book when you become familiar with the material. (I'm assuming the text being referred to is the two-volume set).

 

[ZapperZ]

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.

The official math courses that I had as an undergrad were 3 semesters of Calculus, 1 semester of Diff. Eq., 1 semester of vector calc, 1 semester of complex analysis. Those are all taken from the Math Dept. In addition, the physics dept. also offered a 2-semester course in mathematical physics (which I found to be a lot more useful than most of the math classes that I took). The text used was Arfken's, which is fine if you already have a good math background, but not good if one is doing a self-study or weak in math. I much prefer the Mary Boas text that I quoted in a previous posting. It is something an undergrad in physics (and engineering) can pick up at the Sophomore level and get to study the math needed in his/her upcoming classes.

Zz.

 

[tornpie]

I've often wonder why they don't guide physics majors more towards becoming formally trained mathematicians. Physics, to a point, can be done with just applied math, but at some point one hits a ceiling that needs pure math to get beyond. Areas in math like differential geometry, real, complex, harmonic, and functional analysis, Lie algebras, etc. come in real handy for a lot of problems. In fact, I'd imagine there are many problems that can't even be comprehended without a suitable math background and other problems that get so messy with lower math that are absolutely elegant using topology and other areas of math.

 

[ZapperZ]

I've often wonder why they don't guide physics majors more towards becoming formally trained mathematicians. Physics, to a point, can be done with just applied math, but at some point one hits a ceiling that needs pure math to get beyond. Areas in math like differential geometry, real, complex, harmonic, and functional analysis, Lie algebras, etc. come in real handy for a lot of problems. In fact, I'd imagine there are many problems that can't even be comprehended without a suitable math background and other problems that get so messy with lower math that are absolutely elegant using topology and other areas of math.

Unfortunately, you're assuming that ALL physicists are going to be theorists! :) I have never studied topology, for example, at least not in the formal sense. And I don't think I needed it nor missed it. [then again, maybe that's because I'm just a lowly experimentalist]

Secondly, and this again is a quote from Mary Boas's text in the Preface:

The question of proper mathematical training for students in the physical sciences is of concern to both mathematicians and those who use mathematics in applications. Mathematicians are apt to claim that if students are going to study mathematics at all, they should study it in careful and thorough detail. For the undergraduate physics, chemistry, or engineering student, this means either (1) learning more mathematics than a mathematics major or (2) learning a few areas of mathematics thoroughly and the others only from snatches in science courses... Now it would be fine if every science student could take the separate mathematics courses in differential equations, advanced calculus, linear algebra... and so on. However, most science students have neither the time nor the inclination to study that much mathematics...

It is for this very reason that many physics departments are offering a course in mathematical physics. It is meant to at least give an overview of the kinds of mathematics that a typical physics student would need while going through a physics program. People who need more (like those String theorists) would certainly take more math classes, but at least, these mathematical physics courses would fulfill the need of giving the students some basic understanding of the tools.

Zz.

 

[tornpie]

Now we've stumbled on to a real relevant problem for mathematics and mathematicians. There are areas in the physical sciences that are easy math problems that yield Nobel prizes. In one of the recent AMS (American Mathematical Society in case anyone didn't know) publications, they had an article about an application in the area of Fourier Analysis that got some chemists Nobel prizes. The particulars escape me, but it laments about the lack of willingness on the part of some mathematicians to work on something that isn't groundbreaking in mathematics. The mathematicians don't want to do the work, and the scientists don't want the mathematical background with all the hassle. Of course it goes on and says that some of the blame lies on the mathematicians for not making themselves and some areas of math more accessible.

I guess I'm of the opinion is more math will make one a better problem solver at whatever area they are in and also that many of the easy problems in the sciences are already solved. It's all a matter of how much time one is willing to invest. The payoff can be substantial. As for you, maybe try to fit in a few courses on rigorous analysis and algebra, then hopefully, you may have to thank me someday when you accept the prize from the committee.

 

[ZapperZ]

Now we've stumbled on to a real relevant problem for mathematics and mathematicians. There are areas in the physical sciences that are easy math problems that yield Nobel prizes. In one of the recent AMS (American Mathematical Society in case anyone didn't know) publications, they had an article about an application in the area of Fourier Analysis that got some chemists Nobel prizes. The particulars escape me, but it laments about the lack of willingness on the part of some mathematicians to work on something that isn't groundbreaking in mathematics. The mathematicians don't want to do the work, and the scientists don't want the mathematical background with all the hassle. Of course it goes on and says that some of the blame lies on the mathematicians for not making themselves and some areas of math more accessible.

I guess I'm of the opinion is more math will make one a better problem solver at whatever area they are in and also that many of the easy problems in the sciences are already solved. It's all a matter of how much time one is willing to invest. The payoff can be substantial. As for you, maybe try to fit in a few courses on rigorous analysis and algebra, then hopefully, you may have to thank me someday when you accept the prize from the committee.

Er... as for ME?

I'm already a "practicing physicist" and have gone through as much mathematics as I care to have. It hasn't "hampered" my productivity considering the rate of publications I have per year. Besides, at this level, one learns what one needs on one's own anyway. My more immediate concern is designing a photocathode with a higher QE than what we have now. You'll understand if trying to "fit in a few courses on rigorious analysis and algebra" is waaaay down on my list of things to do.

And lest you think that the anecdotal cases of mathematics mixing with physics is unique, let me point out that there are MANY areas of study in which it appears trivial and uninteresting to another person in a different area. I am a condensed matter physicist by training, but I am working in the area of accelerator physics. By condensed matter standard, the problems and methodology that accelerator physicists are faced with as far as material science problems are concerned are quite primitive! Most condensed matter physicists are not even aware of the type of problems accelerator physicists are faced with and therefore are not able to contribute their expertise to it. And most accelerator physicists are not aware of what has been known from material science for them to fully exploit. Someone here somehow had the insight to hire a staff that isn't trained in accelerator physics, but rather in CM, to finally deal with the material science issues that they face.

So what you described isn't unique, nor is it unique to just physics.

Zz.

 

[marlon]

ZAPPER, You the man, you should run for president

marlon

 

[vanesch]

let me point out that there are MANY areas of study in which it appears trivial and uninteresting to another person in a different area.

This is indeed true: I've switched domains a few times (started out with theoretical system identification, then did experimental particle physics, then microwave instrumentation, energy transport, synchrotron instrumentation, and now I'm into neutron detection), and my observation has indeed been that people are often locked-up in their specific domain, not knowing that the "difficult problem" they are dealing with has been solved for about 50 years next doors. Usually in the beginning I'm met with a kind of mixture of agressivity and amusement ("hehe, that new guy thinks he's going to be smarter than me, who has 20 years in the field, let him try") usually followed with some incredulity ("how did he manage") until I myself am absorbed in the field and start acting as an "old guy". That's usually the sign I have to switch fields :-)

cheers,
Patrick.

 

[ZapperZ]

This is indeed true: I've switched domains a few times (started out with theoretical system identification, then did experimental particle physics, then microwave instrumentation, energy transport, synchrotron instrumentation, and now I'm into neutron detection), and my observation has indeed been that people are often locked-up in their specific domain, not knowing that the "difficult problem" they are dealing with has been solved for about 50 years next doors. Usually in the beginning I'm met with a kind of mixture of agressivity and amusement ("hehe, that new guy thinks he's going to be smarter than me, who has 20 years in the field, let him try") usually followed with some incredulity ("how did he manage") until I myself am absorbed in the field and start acting as an "old guy". That's usually the sign I have to switch fields :-)

cheers,
Patrick.

Well, to be fair to the accelerator physics people, they ARE aware of the fact that they need to bring in more material science/condensed matter people and expertise into the field. This is especially true in the photocathode research area where more and more condensed matter expertise and techniques are being used to improve both cathode fabrication and characterization. And I will say that I did not encounter the kind of "skepticism" that you described. Practically all accelerator physicists that I've encountered, when they realized of my background, almost unimamously would say "Finally! They hired someone who can do something about this!"

I have a paper that was recently accepted for publication in PRL, and it was a great compliment (at least to me) that both referees wrote in their comments that our work has practical interests in both accelerator physics and material science. As a CM physicist, I see a tremendous area within accelerator physics that I can make contributions to - and that what makes me always look forward to coming into work each morning.

Zz.

 

[quarkman]

"Physics is to Math what Sex is to Masturbation" -Richard Feynman

And didn't he know a lot of mathematics? I am a physicist by choice, but I still love mathematics. I think that both mathematicians and physicists are extra careful in their own domain, but tend to get a little lax when dealing with the other subject. Now if I only had a photographic memory and an instantly understanding one as well, I'd be all set to learn everything I ever wanted to about both subjects.

Also, I would suggest reading the section "Doing too much too soon" inAn Open Letter to the Next Generation by James D. Patterson in the July 2004 edition of Physics Today. I firmly believe hindsight is ALWAYS 20/20, so I take what this guy has to say with great weight.

D

 

[vanesch]

Also, I would suggest reading the section "Doing too much too soon" inAn Open Letter to the Next Generation by James D. Patterson in the July 2004 edition of Physics Today.

Indeed worth reading. I committed a few of his sins too, especially the thing about fighting with superiors, and, with hindsight, he's right !
I still think that *I* was right concerning the issues we fought over, but I do think that it would have helped me better to have more people backing me up when I needed good references I must by now have a reputation of someone who can solve difficult problems, but who is also a difficult problem in itself .
There's probably a balance to find between expressing your ideas and fighting for it on one hand, and keeping good relations with the boss
That said, there are (a lot!) of bosses out there with which this is a difficult act!

cheers,
Patrick.

 

[Dr Transport]

To jump in late, I too am a practising physicist. If you are a mathemetician, theorem, proof, theorem, proof. If a physicist thinks along those lines he is called a Mathematical Physicist. The true physicst thinks along the lines of using only the necessary math to describe the solution to the problem. A theoretical phycisist, I am one, thinks along more mathermatical lines that an experimentalist. I have seen some really first rate experimental guys who would put me to shame mathematically. I have never studied topology, etc,... it is not used in my line of expertise. Group theory of lattices and angular momentum is as far as I have gone.

To get back on the subject of the original post. If a math major wants a text to learn some quantum mechanincs, try the Schaum's outline for a start, it solves all the classic problems then get a copy of Griffiths or Liboff or maybe Cohen-Tannouji (sic). Stay away from Sakauri or Messiah for they assume too much background at the advanced undergrad level. If a person has a decent level of preparation in differential equations, linear algebra, partial differential equations and special functions, they should be able to handle the math OK. The underlying physical intuition will be some challenge. A friend of mine took undergraduate QM then went on to take a PhD in experimental physics, he had no problemns, but he did work like a dog to pass the qualifiers because of his lack of coursework.

In reading along, I agree with Zapper. He has made the points I would have made if I had been in on this from the beginning.

DT

 

[tornpie]

I just got my copy of Sakurai today. I'm going through the first chapter. This stuff so far is child's play to anyone with a bit of grad linear algebra behind them. I like this bra and ket stuff.

 

[vanesch]

I just got my copy of Sakurai today. I'm going through the first chapter. This stuff so far is child's play to anyone with a bit of grad linear algebra behind them. I like this bra and ket stuff.

If you're interested, I've put up some stuff on that book, like summaries and solved exercises. It is at:

http://perso.wanadoo.fr/patrick.vanesch/NRQM_main_page.html

The stuff isn't finished, however. But maybe it is useful.
The course itself is over, maybe there will be a continuation one day, I don't know.

If you find errors, remarks etc.. please let me know.

cheers,
patrick.