1. What is the potential energy and the associated Hamiltonian for the H-atom?

1.      What is the potential energy and the associated Hamiltonian for the H-atom? Draw the potential energy V(r)

2.      **Show that  are eigenfunctions of the Hydrogen atom Hamiltonian. What are their associated eigenvalues? **

3.      Show that  are eigenfunctions of  and

4.    What is the degeneracy of

5.      Draw the radial wave functions and the radial probability distributions associated with

6.      Find the probability of finding the electron within 1 bohr radius of the nucleus in a 1S and 2S state. 

What is the most probable location for an electron in a 1S orbital