{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# p137bp4 - B between the highest and lowest n = 2 levels...

This preview shows page 1. Sign up to view the full content.

Physics 137B, Fall 2007 Problem set 4 : perturbation theory Assigned Friday, 21 September. Due in box Friday, 28 September. Starting this week, some of the problems will be assigned from Bransden. Note that the numbering in the second edition is frequently diﬀerent from the ﬁrst edition. All numbers here refer to the second edition. 1. Bransden 8.1 2. Bransden 8.11 3. Consider the n = 1 and n = 2 levels of the hydrogen atom (pure Coulomb potential). Ignore ﬁne structure corrections. (a) Make an energy level diagram of how these levels (10 in total, including spin) are split by an applied magnetic ﬁeld B , assuming g = 2 exactly. (b) What is the energy splitting in an applied magnetic ﬁeld
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: B between the highest and lowest n = 2 levels? Make sure that your answer has units of energy. 4. What is the numerical value of the Bohr angular frequency ω ab for the spin-up and spin-down states in a magnetic ﬁeld B of 1 Tesla, where H = gμ B B ¯ h S z . (1) Remember that for an electron, g ≈ 2 and μ B = e ¯ h/ 2 m . (b) Suppose that a perturbation is added for times t > 0, of the form H = gμ B B ¯ h S x (2) with B ± B . What is the maximum transition probability in ﬁrst-order perturbation theory, starting in the spin-down state at t = 0, if B = 10-4 Tesla? Plot the transition probability as a function of time. 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online