# Question About Heisenberg Uncertainty Principle

#### omegaz

a) (5pts) Consider a one-dimensional square well with infinitely high potential barriers at x = ±2 × 10−15m as shown
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.

#### ChipB

PHF Helper
This is the third set of questions that you've posted from your exam.