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pset08

# pset08 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall , 2002 Professor Robert W. Field Problem Set #8 DUE : At the start of Lecture on Friday , November 8. Reading : Angular Momentum Handouts . C-TDL , pages 643-676 Problems : 1. CTDL , page 765 , #1. 2. CTDL , page 765 , #2. 3. CTDL , page 768 , #6. 4. Consider the spectrum and dynamics of an alkali atom in electric and magnetic fields , both along the z-axis. You must consider three electronic states , the n 2 S 1/2 ground state , the n 2 P 1/2 and n 2 P 3/2 excited states , and the (n+1) 2 S 1/2 excited state. The Zeeman Hamiltonian is z H = −γ B z ( L z + 2 S z ) . The Stark Hamiltonian is H S = ε z z where the only nonzero matrix elements of z are L = 1 , M L = 0. For both Zeeman and Stark effects , you will want to work in the uncoupled basis set. For the Stark effect , the only relevant nonzero matrix elements are n 2 P,M L = 0,M S z (n + 1) 2 S,M L = 0,M S ≡ µ 1 where µ 1 is independent of M S . The optical excitation Hamiltonian H opt = r ε opt ( i x + j y + k z )

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