PHY471 Fall 2000 Quantum Physics I
Homework set 6 Due date: Wednesday, 10/25/2000

1. [4pt] Momentum operator in energy representation

For the infinitely deep square well evaluate the momentum operator acting on any wavefunction that solves the Schrödinger equation can be written as. Here, y_m(x) are the stationary solutions to Schrödinger equation. Evaluate the coefficients a_m explicitely.

2. [3+2pt] Infinite square well in three representations

a) Ohanian #9, p.94 (Evaluate the Fourier transform explicitly).

b) Plot the functions |y(x)|² and |f(p)|² in suitable intervals.

3. [4+2pt] Finite square well

a) Derive the solutions to the time-independent Schrödinger equation for the finite square well described by the potential in eq. (77) in Ohanian. For the region |x|<L choose a solution that is proportional to sin(ax) and show that the energy eigenvalues are determined by solutions to .

b) Show that in the limit the expression reduces to the energy quantization condition for the infinite square well.

4. [5pt] Ohanian #4, p. 92