I am studying Quantum mechanics at the moment, and so naturally a few questions arise!!! So I will post them in this thread. Cheers for any input, I really appreciate all the help that I get!!! First off: 1. My picture of the Hamiltonian is that it is the total spectrum of possible energy values for a system, but to know what energy state it is actually in, one must perform a measurement on the system.This measured valued would then be an eigenvalue of the Hamiltonian. Is this correct? 2. For the time independent Schrodinger equation in one - dimension, can one find a normalizable solution for any x in the case the E<V (V is the potential)?? I know the graph of such a solution would look like a parabola ( and a parabola heading towards negative infinity also), and so I would presume no, but why not exactly? 3. The solutions to the time indep Schrodinger equation in an infinite well form a complete set. Does this mean ANY function in mathematics? This would in fact be the definition of a Fourier Series in this case....I find that odd and somewhat hard to believe!