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?