1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Prove the energy eigenstates are degenerate

  1. Oct 12, 2016 #1
    1. The problem statement, all variables and given/known data

    Two observables ##A_{1}## and ##A_{2}## which do not involve time explicitly, are known not to commute, ## [A_{1},A_{2}]\neq0, ##
    yet we also know that ##A_{1}## and ##A_{2}## both commute with the Hamiltonian: ## [A_{1},H]=0\text{, }[A_{2},H]=0. ##
    Prove that the energy eigenstates are, in general, degenerate. Are there exceptions? As an example, you may think of the central-force problem ##H=\textbf{p}^{2}/2m+V(r)##, with ##A_{1}\rightarrow L_{z}##, ##A_{2}\rightarrow L_{x}##.

    2. Relevant equations
    ## [A_{1},A_{2}]\neq0, ##
    ## [A_{1},H]=0\text{, }[A_{2},H]=0. ##

    3. The attempt at a solution

    Please read my attached file. I type in latex. I really don't understand why I'm incorrect.

    Thanks in advance!!
     

    Attached Files:

    Last edited: Oct 12, 2016
  2. jcsd
  3. Oct 12, 2016 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    What do you know about the eigenstates of two operators that commute?
    What do you know about the eigenstates of two operators that do not commute?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Prove the energy eigenstates are degenerate
  1. Energy Eigenstates (Replies: 2)

  2. Energy Eigenstate (Replies: 3)

Loading...