Homework 4

This homework is due on Tuesday February 6th. You should submit a PDF of your solutions on myCourses.

Do questions 10.4, 10.5, and 10.7 from Townsend.

Hint: you will need the ground state wavefunction for the hydrogen-like (one electron) atom, which is

\[\braket{\mathbf{r}|1,0,0} = {1\over \sqrt{4\pi}} R_{10}(r) = {1\over \sqrt{\pi}}\left({Z\over a_0}\right)^{3/2} e^{-Zr/a_0}\]

where \(a_0\) is the Bohr radius and \(Z\) is the number of protons in the nucleus, and where the wavefunction is normalized such that

\[\int d^3\mathbf{r} \, |\Psi|^2 = \int dr\, r^2 |R_{10}|^2=1.\]