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Trial function and Eigenfunction...

  1. Oct 22, 2015 #1
    1. The problem statement, all variables and given/known data
    Hello, I just started to study QM, I just have a general question, how to know if a trial function is not an eigenfunction of a hamiltonian (that has the lowest value in a graph) ? - Thanks and sorry for the stupid question.
    2. Relevant equations


    3. The attempt at a solution
    I have an idea, but I am not sure if it is right. Is the trial function a eigenfuction of a hamiltonian, if it gives a value (lowest) which is very close to the ground-state energy?
     

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    Last edited: Oct 22, 2015
  2. jcsd
  3. Oct 22, 2015 #2

    blue_leaf77

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    It is not when the corresponding expectation value of energy does not match any of the eignvalues of the Hamiltonian.
    Again, if this value is not exactly the same as one of the Hamiltonian's eigenvalues, then the tried function is not an eigenfunction.
     
  4. Oct 22, 2015 #3
    Thank you man, I really appreciate your help, much love to you. :smile:
     
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