852HW5 - PHYS852 Quantum Mechanics II Spring 2009 HOMEWORK ASSIGNMENT 5 1[20 pts The goal of this problem is to compute the Stark effect to

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Unformatted text preview: PHYS852 Quantum Mechanics II, Spring 2009 HOMEWORK ASSIGNMENT 5: 1. [20 pts] The goal of this problem is to compute the Stark effect to first-order for the n = 3 level of the hydrogen atoms. The stark shift is governed by the potential: V E = − eE Z, so that you will be computing the matrix elements ( 3 ℓm (0) ℓ | Z | 3 ℓ ′ m ′ ℓ (0) ) , which vanish unless ℓ ′ = ℓ ± 1 and m ′ ℓ = m ℓ . a.) Write the matrix element ( 3 ℓm (0) ℓ | Z | 3 ℓ ′ m ′ ℓ (0) ) out as an integral over r,θ,φ . Evaluate the integral for all transitions which obey the selection rules. b.) List all of the degenerate | nℓm (0) ℓ ) states in the n = 3 subspace. Then use the selection rules to group the levels into closed sets of couples states. c.) For each group in part b.) with more than one element, find the ‘good’ eigenstates, by diago- nalizing V E in the subspace of the states in the group....
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.

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852HW5 - PHYS852 Quantum Mechanics II Spring 2009 HOMEWORK ASSIGNMENT 5 1[20 pts The goal of this problem is to compute the Stark effect to

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