Lecture_19

Lecture_19 - PHYS 342 Fall Fall 2011 Lecture 19: Radiative...

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PHYS 342 all 2011 Fall 2011 Lecture 19: Radiative Transitions, dsorption and Emission of Photons Adsorption and Emission of Photons, Selection Rules E 2 21 EE f E 1 h Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 19 1
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How might a wavefunction change with time? Putting time back into the Schrödinger Equation recall from Lecture No. 5 (,) [] xt t something   or x t something  t t the “t” part the “x” part () () () it Let x t x f t x e ) en i x t  2 ( , ) then t 
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 Multiply both sides by : i ii t E t         An operator The operating on Ψ eigenvalue   . . . (,) () E it So xt xe   3
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Why is a photon emitted?   / ) ( ) iE t t re  2 2 2 22 / ** 2 ( , )( (,) () t rt    A. When an electron is in one eigenstate  * 0 // * 2 ( , , ) t t rr t r r t dr e d r     E 2 0 * indepe rd ndent of time r  B. What if an electron could e in o igenstates E 2 0 be in two eigenstates? ) et r t r r t  ? E 1 12 ( , , , ) Let a tr b  ? *2 1 a a a probability that electron is in state E b b probability that electron is in state E  2 b b b p obability that elect on is in state 4
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*   What is expectation value of position r?  0 ** 12 1 2 0 ( , )( , ) (,) rr t r r t dr a rt b rt r a rt d r    1 **** 2* 2 11 21 2 0 / * () () () iE ra b r t r t b a r t r t br tr ar t a dr r be r r t     22 1 // / * 2 1 2 ( ) ti E t i E E t brr re b a d r     1 1 1 2 0 00 * () ( () ( ) ) b r rd r r r r      1 2 t t t t ab r r e e ba r r e r ': c o s s i n c o s s i n i i dr EE Euler s theorem i i e e   2 1 ** ** 0 0 s in os ) c ( E E E E r ab r r ba r r dr i t r ab r r ba r r dr real part of r contains a t t         cos cos(2 ) cos 2 e tf rm that varies with ti t me as t  h 5
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E t Summary Energy Position    2 2 1 / 2 / (,) () ) ( ) iE t rt re t  E 2 ?
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Lecture_19 - PHYS 342 Fall Fall 2011 Lecture 19: Radiative...

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