Homework set 6 Due date: Wednesday, 10/25/2000

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

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

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.