January 13, 1998

PHY 741 - Problem Set # 1

1.

Derive the form of the Schrödinger equation for an electron in a uniform magnetic field: ${\bf{B}}=B_0{\bf{\hat{z}}}$ using the symmetric vector potential ${\bf{A}}=\frac{1}{2} B_0(x {\bf{\hat{y}}} - y {\bf{\hat{x}}})$.

2.

Show that the eigenfunctions of this Schrödinger equation are related to that corresponding to the vector potential ${\bf{A}}= - B_0 y {\bf{\hat{x}}}$ by a phase factor.

3.

Determine the eigenvalue spectrum for form #1 and show that it is consistent with #2.