# To find the energy eigenvalues in the 3D Hilbert space

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1. Sep 10, 2017

### Double_Helix

A fictitious system having three degenerate angular momentum states with $\ell=1$ is described by the Hamiltonian $$\hat H=\alpha (\hat L^2_++\hat L^2_-)$$ where $\alpha$ is some positive constant. How to find the energy eigenvalues of $\hat H$?

Last edited by a moderator: Sep 10, 2017
2. Sep 10, 2017

### Orodruin

Staff Emeritus
How would you usually find the eigenvalues of an operator?

Also, the end tag is [/tex], not [\tex]. Or you can just use double hashes (##) for both tags instead.

3. Sep 10, 2017

### Double_Helix

1. I tried to write the matrix form of the operator.

4. Sep 10, 2017

### Orodruin

Staff Emeritus
And that looked like? What did you do after that?