Good book to understand eigenvalue for quantum mechanics?

[e-pi]

Guys

I read a little on how Heisenberg's quantum mechanics equations (solving with eigenvectors) were derived in the book "What is quantum mechanics: A physical adventure". There is no exercise in the book.

After reading, I still don't understand eigenvalue. What is it for? How to use it? It seems like some kind of magical tool that can solve ALL calculation problem. Is it something like algebra, only in matrix form?

Then I read this tutorial:
http://algebra.math.ust.hk/eigen/01_definition/lecture2.shtml"

My reaction is: so..?

Any good book/link out there that shows eigenvalue application/example?

Btw, is eigenvalue under group theory or more under matrix?

 

[malawi_glenn]

eigenvalues you have both in algebra and calculus.

The link you posted was eigenvalues in Linear Algebra, you have have eigenvalues in calculus. There you don't have eigenvectors, you have eigenFUNCTIONS.

In QM there are many representations, where in one you use Linear Algebra very much and another where you use calculus.

It is not a magic tool that solves all calculation problems.. it is a property of some mathematical systems.

In QM, you have physical states, which are a linear combination of EIGENstates of a particular operator. Each observable (position, energy, momentum, spin etc.) has an operator.

Here you have some good links about QM and eigenvalues etc:

http://farside.ph.utexas.edu/teaching/qm/lectures/lectures.html

http://en.wikipedia.org/wiki/Eigenvalues (look at references)

Any introductory QM book will help you also, try Griffiths.

 

[cgw]

Thats funny. I first heard the term eigenfunction and eigenvalue in a modern physics course/book (wave function). Later I read the book you are referring to which basically developes quantum mechanics from Heisenbergs point of view using matricies. I ended up going through the Linear Algebra course at MIT opencourseware as I had never taken Linear Algebra in school. Eigenvales and eigenvectors are a big part of the course so I am hopefully getting a clue. (actually I am 2/3's the way through though I just got side tracked by Fourier series) I am going through it in hopes of increasing my understanding of quantum mechanics, but it was immediately apparent that it is usefull for much more than physics.