in figure a. For a proton in this well use the Hiesenberg Uncertainty Principle to derive the minimum uncertainty in the

momentum and then use this to obtain an estimate of the minimum kinetic energy, also called the zero point energy, for the

proton.

b)(5pts) Use the Schrodinger Equation to obtain the energy and wavefunctions for the lowest two energy levels for the

proton in this infinite square well. Do these satisfy the zero point energy?

c)(5pts) Consider the case where one side of the barrier is infinite while the other has a barrier that is of finite height U0

and narrow width σ as shown in figure b. Discuss the behaviour of the wavefunction inside the well [region 1] inside the

barrier [region 2], and outside the barrier [region 3] for two eigen energies, E1 < U0 and E2 > U0.

d)(5pts) What are the boundary conditions required for the wavefunction at the boundaries between the three regions?

e)(5pts) Mention at least one example in physics where one has a barrier of the type shown in figure b, and mention the

experimental consequences.