Trial function and Eigenfunction....

Ronf
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Homework Statement


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.

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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? [/B]
 

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Ronf said:
how to know if a trial function is not an eigenfunction of a hamiltonian (that has the lowest value in a graph) ?
It is not when the corresponding expectation value of energy does not match any of the eignvalues of the Hamiltonian.
Ronf said:
Is the trial function a eigenfuction of a hamiltonian, if it gives a value (lowest) which is very close to the ground-state energy?
Again, if this value is not exactly the same as one of the Hamiltonian's eigenvalues, then the tried function is not an eigenfunction.
 
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Thank you man, I really appreciate your help, much love to you. :smile:
 

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