Question

The infinite potential well has zero potential energy between 0 and a, and is infinite elsewhere.

a) What are the energy eigenstates of this quantum system, and what are their energies? In the case of a discrete spectrum, explain where the quantization comes from.

b) Suppose we take the wavefunction at a given time to be an arbitrary function of x that is symmetric around the center of the well (at x = a/2). Is this a stationary state in general? Briefly explain your answer.

c) Start with the wavefunction of b), measure the location, and then wait for an hour and measure the energy of the state. Which outcomes are possible?

d) Suppose we start with the particle in its groundstate. At some point the well doubles in size, and extends from 0 to 2a (while the wavefunction is still given by the groundstate of the smaller well). What are the possible outcomes of an energy measurement of this system?

Answer 1