Quantum Engi Q and A_Part_48

Quantum Engi Q and A_Part_48 - 142 APPENDIX A. ADDENDA...

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142 APPENDIX A. ADDENDA A.21.3 Corrected multipole matrix elements A.21.4 Matrix element ballparks A.21.5 Selection rules A.21.6 Ballpark decay rates A.21.7 Wave functions of deFnite angular momentum A.21.8 Weisskopf and Moszkowski estimates A.21.9 Errors in other sources
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A.22. DETAILS OF THE ANIMATIONS 143 A.22 Details of the animations A.23 WKB Theory of Nearly Classical Motion A.23.1 Solution wkb-a Question: Use the equation 1 ¯ h i x 2 x = x 1 p c ( x ) d x = to fnd the WKB approximation For the energy levels oF a particle stuck in a pipe oF chapter 3.5.5. The potential V is zero inside the pipe, given by 0 x x In this case, the WKB approximation produces the exact result, since the classical momentum really is constant. IF there was a Force feld in the pipe, the solution would only be approximate. Answer: Substituting in p c = 2 mE , x 1 = 0 and x 2 = x , 1 ¯ h 2 mEℓ x = and squaring both sides, the energy is Found as E = n 2 ¯ h
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This note was uploaded on 11/13/2011 for the course PHY 4458 taught by Professor Garvin during the Fall '11 term at University of Florida.

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Quantum Engi Q and A_Part_48 - 142 APPENDIX A. ADDENDA...

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