There's an electron in a one-dimensional potential well of width Lz in the z direction, with infinitely high potential barriers on either side (i.e., at 0 z = and z L = z ). Assume that the potential energy is zero inside the well. Suppose that at time t = 0 the electron is in an equal linear superposition of its lowest two energy eigenstates, with equal real amplitudes for those two components of the superposition.
Starting with the normalized wavefunction at time t = 0, write down an expression for the wavefunction valid for all times t and show whethere this wavefunction is normalized for all such times t