Here is one of my test question. I did it wrong. Specify whether the following statement is true or false and explain why? "The time independent Hamiltonian operator 'H' acting on an allowed state Psi will give the same state back, i.e "H Psi=E Psi, where E is the energy of the given state." The answer is false. I don't know why but its false. Can any one explain me this? Thank you.