Homework   #10 (due 4/22/08)

1.       Hyperfine structure of H and D.

Go to  Phys. Rev.  72, 971 (1947) to find out  the hyperfine separation for the ground electronic state of  atomic hydrogen and deterium.  Copy down the answer from their paper. Take a look at Fig. 1 of this paper.  You may want to take a look at the seminal paper by  I. I. Rabi also.

(a)    Express the hyperfine separation in terms of  electron volts, and in terms of the wavelength (in cm).

(b)   Go to a textbook or web to find out the Hamiltonian that describes the source of the hyperfine interaction in H and D.

2.       Identify the Hilbert space of the atomic hydrogen in the following successive approximations.

(a)    Treat the electron without spin.

(b)   Include the fact that electron has spin but no spin-orbit interaction.

(c)    Include the fact that there is spin-orbit interaction.

(d)   Include the fact that the proton also has spin.

3.        Explain in words the origin of

(a)    Spin-orbit interaction.

(b)   Hyperfine interaction.

4.       In sodium, there are two well-known lines, called D1 and D2 lines.  They have wavelenth of 589.6nm and 589.0 nm.  Identify what states are involved for these  two lines.  (You can start with Wikipedia for references) .

Fig. 2 and Fig. 3 of this report  show  the fine and hyperfine structure of this system.  These spectroscopic data are needed for laser cooling involving Na.  Copy down the level sparations in THz or GHz up to three digits accuracy. You may want to think about the selection rules.

5.       Merzbacher, exercise 11.21. page 252.

6.       Problem 4, of Merzbacher, p. 255.