To find the energy eigenvalues in the 3D Hilbert space

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SUMMARY

The discussion focuses on finding the energy eigenvalues of a Hamiltonian operator defined as \(\hat H=\alpha (\hat L^2_++\hat L^2_-)\) for a system with three degenerate angular momentum states where \(\ell=1\). Participants emphasize the importance of constructing the matrix representation of the operator to facilitate the calculation of eigenvalues. The conversation also highlights the need for clarity in notation, specifically the correct use of end tags in LaTeX formatting.

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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##?
 
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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.
 
  1. Orodruin said:
    How would you usually find the eigenvalues of an operator?
    I tried to write the matrix form of the operator.
 
ZeroFuckHero said:

  1. I tried to write the matrix form of the operator.
And that looked like? What did you do after that?
 

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