Mathematics for Quantum Mechanics/Thermodynamics/Statistical Mechanics

[bacte2013]

Hello!

I am a rising sophomore with a major in microbiology. Although my main interest is in the microbiology and biochemistry, I am also deeply fascinated by the atomic/quantum physics, relativity, thermodynamics, and statistical mechanics. I will be taking those courses later on. I wrote this post to ask you what should I know in terms of mathematical subjects for those math-intensive courses; they are introductory courses. Do I need to know the proof-based, theoretical mathematics or am I fine with the computational mathematics? Do I need to know how to do the mathematical proofs for those courses?




MSK

 

[Matterwave]

For an introductory course, you certainly don't need the rigorous proof based mathematics. You should have a working knowledge of calculus (single and multi-variable), linear algebra, and differential equations. That should be about it.

 

[bacte2013]

Thank you very much for the response! So I do not need to know the calculus levels of Spivak and Apostol for those introductory courses?

 

[Matterwave]

Introductory courses require working knowledge. More advanced courses may require some more rigorous knowledge. But at no point in physics do you probably really ever need the total rigor of a mathematician, unless you plan on doing mathematical physics, or applied math. Not to say that it wouldn't help to be rigorous, but most physicists are not so concerned with rigor.

I am not familiar with those books, so I can't comment on their levels.

 

[micromass]

Thank you very much for the response! So I do not need to know the calculus levels of Spivak and Apostol for those introductory courses?

No, definitely not.

For QM, I would advise you to read up on vector spaces, linear operators, inner-product spaces and maybe even dual spaces. This will help a great deal.

A bit of mathematical probability theory will definitely help for Stat Mech since I've seen that Stat Mech books truly botch the job. But you definitely don't need to go in the nitty gritty details.