Quantum Mechanics for a math major

[PieceOfPi]

Hi,

I will be a senior next year, and I am thinking of taking a physics class that deals with quantum mechanics. I am a math major, and have taken variety of math courses (e.g. real analysis, abstract algebra, complex variables, advanced linear algebra, and etc.) as well as first-year physics course (calc-based). Right now, I am really interested in learning quantum mechanics (and possibly other topics in physics as well, but so far QM seems like the most interesting one), and I have a few options to study this subject:

1. The first quarter of the second-year physics sequence deals with a little bit of relativity and QM. For this course, I have no problem with prerequisites, since I've taken the first-year physics and intro ODE already. The text for this course will likely to be Physics for Scientists and Engineers by Giancoli, which I used in the first-year physics, and thought it was pretty basic. I also had a professor for this course in my first-year physics as well, and I thought he was a good professor. This sequence only deals with QM just for the first quarter--the remainder of the sequence deals with statistical mechanics and thermodynamics (which might be an interesting topic to study as well).

2. There is upper-division QM course for physics major. The prerequisite for this course is upper division EM, but the professor who is teaching this course said it's not necessary (and he thought my math background should be strong enough). The text for this course is Griffiths' Introduction to Quantum Mechanics. Never had this professor before, but I've heard a fair number of positive things about him. And this is a one-year sequence, and it will all be QM.

Personally, I'd like to challenge myself and take the latter sequence, but if that is too challenging for me, I wouldn't mind taking the former option.

Also, despite its coolness, are there any benefits for a math major to take this course? It seems like a lot of math is applied in this field in a pretty interesting way...

Thanks!

 

[ice109]

no offense but your math classes haven't prepared you for qm taught by a physicist.

the way that physicists solve odes and pdes is not the way you learned. the way that physicists do integrals (especially against dirac deltas) will not be familiar to you.

griffiths is an easy book comparatively speaking so you've got that working in your favor but it's just not germane to a math major.

for example: i had taken a full linear algebra sequence before taking qm which is exactly what everyone suggests you know before taking qm and there were still points i didn't understand. specific example: i knew gram schmidt orthonormalization up and down and i still don't get degenerate perturbation theory.

my suggestion to you: study it on your own (from shankar's principle's of quantum mechanics)

edit: i took the class with the same qualifications as you

 

[PieceOfPi]

ice109: Thanks for your honest opinion. I will keep that in my mind when I finally decided what to take next fall.

Any other thoughts?

 

[deRham]

PieceOfPi, the previous poster had it right - mathematicians think and work differently. You might enjoy self-study as he said, combined with some good books on mathematical physics, such as on quantum field theory.

 

[deRham]

You COULD survive the physics course, but you would have to spend lots of time adapting to the course.

You might consider asking if you can sit in on the lectures, so you can work at your own pace.

 

[PieceOfPi]

I see. So it sounds like the differences between how mathematics is used in physics and math is the major difficulty form me to study QM. That's too bad, since I won't be able to go back in time and study more physics (which is something I kind of wish I have done, but I guess life is like that). So I think as of now, the former option would be the safe bet, since the only prerequisite for this course is the first-year physics and diff eq. I guess I also have an option of taking upper division EM (which only requires multivariable calculus), but I might have hard time seeing how physicists use math as well (although our school recommends students to have EM taken before QM, so that EM course might actually teach how math is being used in physics). Any thoughts?

Thanks for your thoughts. I won't completely erase that QM option yet, but I will certainly keep in mind what you told me so far. More comments are appreciated if you have any.

 

[deRham]

I really think it might be more fun for you as a math major to sit in on the more advanced class. Remember, as a math major you may be able to appreciate some points about advanced physics that other physicists won't, because you'll have the mathematical background. But the physics course will be taught with a physics perspective, probably diminishing the math. I would hunt to find some very involved mathematical physics for the future, after sitting in on the class to learn what it's about [from the proper, advanced perspective].

 

[Landau]

Take advantage of your math knowledge and use a QM book which treats the math with respect, such as Ballentine or https://www.amazon.com/dp/0387953302/?tag=pfamazon01-20.

Use this besides the Griffiths book to read what Griffiths is trying to say in bad language. I think you can do just fine; a first QM course usually is difficult for physics students because there is little physical intuition (as opposed to, say, mechanics) involved. For a math student this can be an advantage, as long as you don't let the perverse treatment of functional analysis by phycists confuse you :)

 

[deRham]

Yeah, Landau's suggestion is what I was trying to make, but with more clarity, given I know less about physics probably.

Quantum is certainly a lot of math, and in fact there are mathematical discussions of how best to model its theory all the time, because that's really part of the point. If it were easy to describe intuitively, it would not be of the nature it is. Not only precise mathematics, but the question of what kind of precise mathematics and language to work in really is important.