Homework #9  (due 4/15/08)

9.1.  Do the three exercises 14.1, 14.2 and 14.3 given on page 14-8.

9.2. (a) Show that a constant magnetic field B can be expressed in terms of vector potential A,

With

Write down the time-independent Schrodinger equation (in Cartesian coordinates) for an electron (electron  charge q=-e)  in a constant magnetic field B which is pointing along the +z-axis.

(b) Show that the same constant magnetic field B along the z-axis can also be expressed with the vector potential  Ax=-B y, and Ay=Az=0,  Write down the Schrodinger equation using the present form of the vector potential, and show that the differential equation is separable. Find the energy and the eigenfunction of this problem . (Hint: the motion along y is the same as in a harmonic oscillator.)