Good book to understand eigenvalue for quantum mechanics?

In summary, the conversation discusses the concept of eigenvalues and eigenvectors and their application in various fields such as quantum mechanics, linear algebra, and calculus. The participants also mention resources for further learning about eigenvalues and their properties.
  • #1
e-pi
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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?
 
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  • #2
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.
 
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  • #3
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.
 

Related to Good book to understand eigenvalue for quantum mechanics?

1. What is an eigenvalue in quantum mechanics?

In quantum mechanics, an eigenvalue is a number that represents the possible values of a physical quantity in a given quantum state. It is the result of applying a mathematical operator to a quantum state, and it tells us the possible outcomes of a measurement of that state.

2. Why is understanding eigenvalues important in quantum mechanics?

Eigenvalues are important in quantum mechanics because they allow us to calculate the probabilities of different outcomes of measurements, which is a fundamental aspect of quantum theory. They also help us understand the behavior of quantum systems and how they evolve over time.

3. How can I use eigenvalues to solve problems in quantum mechanics?

To solve problems in quantum mechanics using eigenvalues, you first need to identify the relevant operators and eigenstates for the system you are studying. Then, you can use the eigenvalue equation to find the possible eigenvalues and corresponding eigenstates. Finally, you can use these values to calculate probabilities and make predictions about the behavior of the system.

4. What are some common applications of eigenvalues in quantum mechanics?

Eigenvalues are used in many different applications in quantum mechanics, such as calculating energy levels of atomic and molecular systems, predicting the behavior of quantum particles in a potential well, and understanding the dynamics of quantum systems in time-dependent situations.

5. Are there any recommended books for understanding eigenvalues in quantum mechanics?

Yes, there are several books that are highly recommended for understanding eigenvalues in quantum mechanics, such as "Quantum Mechanics" by David Griffiths, "Introduction to Quantum Mechanics" by David J. Griffiths and Darrell F. Schroeter, and "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili.

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