1165_Physics ProblemsTechnical Physics

1165_Physics ProblemsTechnical Physics - 506 P41.42 Quantum...

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506 Quantum Mechanics P41.42 (a) Use Schrödinger’s equation =− 2 22 2 ψ x m EU = af with solutions 1 11 =+ Ae Be ik x ik x [region I ] 2 2 = Ce ik x [region II ]. FIG. P41.42(a) Where k mE 1 2 = = and k mE U 2 2 = = . Then, matching functions and derivatives at x = 0 ψψ 1 0 2 0 bg bg = gives ABC += and d dx d dx 1 0 2 0 F H G I K J = F H G I K J gives kAB kC 12 −= . Then B kk A = + 1 1 21 and C A = + 2 1 . Incident wave Ae ikx reflects Be ikx , with probability R B A == + = + 2 2 2 2 2 2 1 1 bg . (b) With E = 700
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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