Question

Consider an electron in a one-dimensional potential well of width L_z in the z direction, with infinitely high potential barriers on either side (i.e., at z = 0 and z = L_z ). For simplicity, we assume 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.

(i) Write down the wavefunction at time t = 0 such that it is normalized. (ii) Starting with the normalized wavefunction at time t = 0 , write down an expression for the wavefunction valid for all times t. (iii) Show explicitly whether this wavefunction is normalized for all such times t.

Answer 1