# Help Finding eigenvalues of angular momentum operators

1. May 11, 2010

### thebigstar25

urgent help!!.. Finding eigenvalues of angular momentum operators

the question is asking to find the eigenvalues of:

3/5 Lx - 4/5 Ly ...

I feel that i have to connect it with the L^2 and Lz operators but i just have no idea how to start .. any suggestions will be greatly appreciated ..

2. May 11, 2010

### Mindscrape

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

Why is there a ..., is there more to the problem?

If you know the matrix forms of the operators (are you in 2D, 3D, what?), then all you have to do is subtract and diagonalize.

3. May 11, 2010

### thebigstar25

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

... R just dots , and im supposed to do it without considering the matrix form :(

4. May 11, 2010

### Mindscrape

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

Ah, okay, take a general ket and work with it then.

You should know L^2|l,m> and Lz|l,m> and that L^2=Lx^2+Ly^2+Lz^2

5. May 11, 2010

### thebigstar25

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

that what I was confused about .. how would I apply L^2=Lx^2+Ly^2+Lz^2 in order to find 3/5 Lx - 4/5 Ly , since the expression I have without "square" .. im not sure how to connect them together..

6. May 11, 2010

### vela

Staff Emeritus
Re: urgent help!!.. Finding eigenvalues of angular momentum operators

Once you know the answer, it seems like it should have been obvious. One suggestion is to think about rotations.

A different approach would be to write Lx and Ly in terms of the ladder operators L+ and L-, but I'm not sure how this way works out.

7. May 11, 2010

### thebigstar25

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

i tried ur second suggestion but things got messy there .. How would i make use of the symmetry along z axis..

8. May 11, 2010

### nickjer

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

Does it only ask for eigenvalues, or eigenvectors as well? Because eigenvalues are very simple to get using rotations as vela noted.

Last edited: May 11, 2010
9. May 12, 2010

### thebigstar25

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

it is just the eigenvalues .. My problem is that im not sure how to apply that to my question .. Anyway, this question from an old homework and i just wanted to know how to solve it ..

10. May 12, 2010

### nickjer

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

First, do you know what the rotation operator for angular momentum is? Since that will help you solve this problem.

11. May 12, 2010

### thebigstar25

Re: urgent help!!.. Finding eigenvalues of angular momentum operators

no i dont know, or maybe i do but i dont know that it is called rotation operator?.. Im not sure :/