385lec5 - PHYS 385 Lecture 5 - Schrdinger equation for a...

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PHYS 385 Lecture 5 - Schrödinger equation for a free particle 5 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 5 - Schrödinger equation for a free particle What's important : Schrödinger equation for a free particle Text Gasiorowicz, Chap. 3 In the previous lecture, we proposed a candidate function that had many of the attributes that we desire for a wave packet. Starting with the momentum distribution, g ( k ) = exp(- [ k - k o ] 2 ) (not normalized) we use the transformation for stationary packets f ( x ) = - + g ( k ) exp( ikx ) dk = - + exp(- [ k - k o ] 2 ) exp( ikx ) dk to obtain f ( x ) = exp(- x 2 /4 ) • exp(+ ik o x ) ( π / ) 1/2 . (not normalized, stationary) For moving wavepackets, we started with f ( x , t ) = - + g ( k ) exp( ikx - i t ) dk , (1) and then removed in favour of k through the relation = E / h = ( h / 2 m ) k 2 , (2) which we found from E = h (3) and the de Broglie hypothesis p = h k = h
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This note was uploaded on 09/07/2009 for the course PHYS 385 taught by Professor Davidboal during the Spring '09 term at Simon Fraser.

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385lec5 - PHYS 385 Lecture 5 - Schrdinger equation for a...

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