To find the energy eigenvalues in the 3D Hilbert space

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Homework Help Overview

The discussion revolves around finding the energy eigenvalues of a Hamiltonian operator in a three-dimensional Hilbert space, specifically for a system with three degenerate angular momentum states characterized by a given Hamiltonian.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss methods for finding eigenvalues of operators, with some attempting to express the operator in matrix form. Questions arise regarding the steps taken after forming the matrix representation.

Discussion Status

The discussion is ongoing, with participants sharing their approaches and seeking clarification on the process of finding eigenvalues. There is an exchange of ideas about the representation of the operator and the next steps in the analysis.

Contextual Notes

Participants note potential issues with notation, specifically regarding the use of end tags in mathematical expressions.

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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