Trial function and Eigenfunction....

[Ronf]

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.

Homework Equations

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]

 

[blue_leaf77]

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.

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.

 

[Ronf]

Thank you man, I really appreciate your help, much love to you.