1. Plot the wave function and square of the wave function for the three lowest energy levels of an harmonic oscillator having the mass of a proton and a force constant of 1 m dyne per Angstrom unit.

2. A certain stationary state has the wave function where N is the normalization constant. Find the system’s potential energy function and its energy. (Hint: Substitute in the Shrodinger equation. Assume that V = 0 at the origin, this only shifts all energy levels without affecting the level spacings)

3. Evaluate for the harmonic oscillator.

4. Make plane polar graphs of ANY ONE p-orbital and ANY ONE d-orbital. You may print and use this polar graph paper. Mark enough points and join by smooth lines. Mark the Cartesian axes.