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# hw.4 - between levels of 0.20 eV Assume the dipole to be eX...

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Physics 829 Spring 2001 Dr. Herbst Homework Assignment # 4 Due: 27 April 2001 1) Consider an electron bound in the ground state of a one-dimensional box (-a/2 x a/2) of finite height V 0 . Assume that the ground state can be represented by a particle in a box of infinite height. Determine the rate of escape of the particle as a function of the radiation field frequency ϖ . You may assume that the final momentum is large. Use plane wave continuum functions for the escaped particle. W(x,t) = 2ex ε cos ϖ t 2) Calculate the Einstein A coefficient as a function of level for a one- dimensional harmonic oscillator of mass 5 amu and an energy separation
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Unformatted text preview: between levels of 0.20 eV. Assume the dipole to be eX. Use cgs units. 3) Determine the 1s <--> 2p absorption, stimulated emission, and spontaneous emission rates (s-1 ) for H atoms in the solar photosphere (T = 6000 K). Which is the larger emission rate? 4) Use Fermi’s Golden Rule for time-independent perturbations to derive the Born Approximation for elastic collisions. Use box normalization. Your final result should be: ( ) = 2 4 2 h 4 | exp(-i { k f-k i ∫ } • r ) V ( r ) d | 2...
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