1.     In 270 or perhaps intro-quantum you discover that the momentum operator can be represented in a one dimensional world as

Show that for the given a wave function

that this is an eigenfunction of the momentum operator.

2.     Construct a spin 1/2 wavefunction as a column matrix. Use the pauli spin matrices to define  find which of these operators commute. Find the column matrix states that are eigenstates of  .

3.     Consider a hydrogen atom in its ground state so that the orbital angular momentum of the composite system is  Find the possible angular momentum states assuming that both particles are spin 1/2.  (This is such a standard problem that you will be able to find it in a million places. Please read through a few of these treatments and write down any confusion).

 

Bring at least one question to class relating to the addition of spin.