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exam.2000 - τ Use time-dependent perturbation theory(first...

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Physics 829 Spring 2000 Dr. Herbst MIDTERM EXAMINATION (In Class; Closed Book) 12 MAY (100 POINTS) 1) (20 points) A one-dimensional harmonic oscillator is subjected to a perturbation of the type ax 3 . Use stationary perturbation theory through second order to determine the correction to the ground state energy. E n = h ( n + 1 /2); ( x ) n , n + 1 = { h ( n + 1) 2 } 1 / 2 2) (40 points) Find the best value for the ground state energy for a particle of mass m in the gravitational potential: V = gz ; z 0; V = ∞ ; z < 0 with the variational trial function z exp( - az ) . Then compare your answer with that obtained from the WKB approach. 3) (40 points) a) (12 pts) A hydrogen atom in its 1s state is placed in a static electric field directed along the z-axis for a time
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Unformatted text preview: τ . Use time-dependent perturbation theory (first order) to determine the probability of transition to the 2p level as a function of τ . <2p |ez|1s> = 0.74ea . E n = -e 2 / 2 a n 2 b) (12 pts) How does your answer to a) change if instead of a static field, monochromatic radiation of resonant frequency ϖ is used? c) (16 pts) How does your answer to b) change if instead of monochromatic radiation, a range of frequencies centered on the resonant frequency is used? Do not use the infinite time limit. For part (c), assume a flat distribution function g( ϖ )d ϖ and integrate over all frequencies....
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