Issued Wed, Nov 26 Due Wed, Dec. 3

Reading for this week: Ch. 12

There are HINTS for this homework.

These problems can be done even if we haven't covered all of the details of the solutions of the hydrogen atom wavefunctions. All you really need are the normalized radial wavefunctions themselves, Eq. 12-30. (and of course an understanding of the Ylm's from previous chapters.)

1) Gas 12-2

2) Gas 12-5

3) Gas 12-6

Note: You only need to "write out an expression". You should do the required angular integrals, but you needn't bother actually doing the radial integral. (Do try to set it up, with correct factors of 2 and Pi, and limits of integration, etc.) (I don't believe the integral is even doable in closed form?!)

4a) Find <r> and <r^2> for an electron in the ground state of a hydrogenic atom. (Express your answer in terms of Z and a0, the Bohr radius). Do not assume Gas. Eq. 12-36, but you may use Gas 12-30.

b) Find <x> and <x^2> for an electron in the ground state of hydrogen. (Hint: No new integrals are required! Use , and exploit the symmetries of the ground state)

c) Find <x^2> for the state n=2, l=1, m=1.

(Note: This state is NOT symmetric. x=r sin(theta) cos(phi) should help...)

(Extra Credit: Gas. 12.10.)