Expectation values and energy.

There was a really interesting question, from a person in the back row on the right, on Tuesday

regarding the relationship between the energy, $E_1$, which is both a parameter in the time-independent Schrodinger equation and the eigenvalue of the energy operator when applied to the ground state wave function. For the finite square well, and in most cases, $\psi_1$ is an energy eigenstate, but not an eigenstate of kinetic energy. This video explores the relationship between the energy, $E_1$ and the expectation values of the kinetic and potential energy.