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Time Dependent Perturbation Theory Homework Hotline

Physics 519 Homework Set #3 Spring 2013 Due in class 4/24/13 300 pts 1. (100 pts) Sakurai 5.35. Simplified photo-electric effect. You do not need to repeat steps worked out in Sakurai (and also in lectures) to obtain a general formula for the transition rate. The point here is to calculate the resulting matrix elements and obtain a fully explicit expression for the rate and angular distribution. The ground state of a hydrogen atom ( n = 1, l = 0) is subjected to a time-dependent potential as follows: V ( ~x, t ) = V0 cos( kz-ωt ) . Using time-dependent perturbation theory, obtain an expression for the transi-tion rate at which the electron is emitted with momentum ~ p . Show, in particular, how you may compute the angular distribution of the ejected electron (in terms of θ and φ defined with respect to the z-axis). Discuss briefly the similarities and the differences between this problem and the (more realistic) photo-electric effect. Note: The initial wave function is given by ψ n =1 ,l =0 ( ~x ) = 1 √ π ± 1 a0 ² 3 / 2 e-r/a0 . The final wave function, at least in a very large box of size L , can be approxi-mated to be ψ f = ± 1 L 3 / 2 ² e i~ p · ~x/ ¯ h . incoming light is ignored by considering the perturbation V ( ~x, t ) = V0 2 ³ e i ( kz-ωt ) + e-i ( kz-ωt ) ´ . The e-iωt term leads to absorption of energy by the atom and thus (if the energy exceeds the ionization threshold) to ejection of a pho-toelectron. Following Sakurai’s development or our class notes, one finds, us-ing Fermi’s Golden rule (FGR), that the transition rate into electrons with momentum with solid angle d Ω of ~ p f is dw d Ω = 2 π ¯ h |{z} FGR mp f ¯ h 3 ± L 2 π ² 3 | {z } density of states µ µ h ~ p f | ( V0 / 2) e ikz | i i µ µ 2 | {z } matrix element . The required matrix element is h ~ p f | e ikz | i i = 1 L 3 / 2 Z d 3 xe-i~ p f · ~x/ ¯ h e ikz 1 √ π ± 1 a0 ² 3 / 2 e-r/a0 = 1 √ π ( a0 L ) 3 / 2 Z d 3 xe-i~ q · ~x e-r/a0 , 1

Quantum Mechanics Assignment Help

Quantum Mechanics is a field in physics that deals with electrons, protons, neutrons, atoms and photons. Mathematics can define the dual particle-like and wave-like behaviour and interactions of energy and hence it plays a major role in quantum physics. The popular properties and concepts in quantum mechanics on which most of the problems are based are electron spin quantum, quantum mechanics model of an atom, photon polarization, operator factorization, energy eigenstates, perturbation theory, infinite square well, simple harmonic oscillator, K-mesons, Stern-Gerlach and rotations and symmetries.

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