What can you do with the Schrodinger equation?

Describe the solution to the Schrodinger equation for a free particle.

Show how the quantum energy levels for a particle in a box come about.

Compare the energy levels for an infinite square well potential with those of a finite well.

How are the quantum energy levels obtained for a finite potential well?

Show how to calculate the tunneling probability through a barrier.

Describe the energy levels of a quantum harmonic oscillator.

Show how to set up the Schrodinger equation in three dimensions.

What can be learned from the time dependent Schrodinger equation?