Mathematical prerequisites for Quantum Mechanics

[D.K.]

So, I am about to read Landau's and Lifschitz's textbook on Quantum Mechanics. What kind of mathematics I should be already familiar with in order to completely understand the above mentioned material?

Thanks for all the advice.

 

[LostConjugate]

Algebra, Linear Algebra, Calculus, and Differential Equations

If you want to power through it all, you can do so here in possibly the most efficient form.

http://tutorial.math.lamar.edu/

 

[A. Neumaier]

So, I am about to read Landau's and Lifschitz's textbook on Quantum Mechanics. What kind of mathematics I should be already familiar with in order to completely understand the above mentioned material?

Since you are already about to read it, just start, and note while reading the concepts you are not yet sufficiently familiar with. Then look these up and practice their use.
This recipe works for anything you read at anytime, and it gives you precisely the minimal amount that you need.

Alternatively, first read (and practice with) books about vector analysis, ordinary and partial differential equations, functional analysis, differential geometry, etc.. This will give you a much better grounding for the long run, but will be much more than what you need at first.

 

[dextercioby]

Another thread on <mathematical prerequisites>. Well, all depends on how deep in knowing and understanding a particular physical theory you wish to get. L & L's book does indeed teach you a lot of physics and phenomenology at the price (but most books pay this price) of keeping mathematical rigor to a mininum.

So yes, linear algebra and calculus: real and complex + Fourier transformations should be handled decently before going to an involved reading of the book you mention.

 

[D.K.]

L & L's book does indeed teach you a lot of physics and phenomenology at the price (but most books pay this price) of keeping mathematical rigor to a mininum.

Well, that's quite surprising to hear. Would you be so kind as to recommend a quantum mechanic textbook that in your opinion is the best when it comes to math rigor?

 

[Fredrik]

Well, that's quite surprising to hear. Would you be so kind as to recommend a quantum mechanic textbook that in your opinion is the best when it comes to math rigor?

I don't think there are any rigorous QM books. The problem is that it would take a typical QM student at least a year, probably two, to learn all the math (in particular topology and functional analysis) they need to understand the mathematics of QM.

People always mention differential equations in these threads. (There are lots of them). I always feel compelled to say that there's only one differential equation in the theory, and the QM book will tell you how to solve it. So studying a book on differential equations won't help you at all to prepare for QM, other than by giving you some mathematical maturity. You're much better off studying linear algebra. I recommend Axler.

 

[A. Neumaier]

Would you be so kind as to recommend a quantum mechanic textbook that in your opinion is the best when it comes to math rigor?

Reed and Simon, Methods of Modern Mathematical Physics. 4 Vols.
(This includes all functional analysis needed.)