1. The problem statement, all variables and given/known data A particle moves in a one dimensional potential : V(x) = 1/2(mω2x Show that the function ψ(x) = a0exp(-βx2) is an eigenfunction for the Hamiltonian for a suitable value of β and calculate the value of energy E1 2. Relevant equations 3. The attempt at a solution What I did was take the Hamiltonian, differentiate twice the function ψ(x) and then sub in the twice differentiated function along with the potential into the Hamiltonian. But there I get confused. Apparently taking a peek at the solutions, it argues that you should set the Hamiltonian to zero and then since it is supposed to be a constant, the x^2 terms cancel out and your final answer is β=mω/2hbar. I have no idea what they have done though! Any one care to explain? Thanks!