# Eigenstate of a spin operator

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1. Mar 6, 2016

### johnpaul543

1. The problem statement, all variables and given/known data
I have a spin operator and have to find the eigenstates from it and then calculate the eigenvalues.
I think I managed to get the eigenvalues but am not sure how to get the eigenstates.

2. Relevant equations

3. The attempt at a solution
I think I managed to get the eigenvalues out to be ±1 by forming the following matrix

2. Mar 6, 2016

### vela

Staff Emeritus
That matrix is wrong. What is $\lambda$? What does $\sin^{\pm i\lambda}$ even mean?

Have you really never found eigenvectors for a matrix? It's typically covered in lower-division linear algebra and differential equations. It seems a bit strange that you'd be in a course asking you to do this problem without having taken the math courses.

3. Mar 6, 2016

### johnpaul543

Apologies the $\sin^{\pm i\lambda}$ is incorrect and meant to say $\sin^{\pm i\varphi}$ and yes I have taken eigenvectors before, just not one similar to this.

4. Mar 7, 2016

### blue_leaf77

That doesn't make sense either.