4thQuiz - PHY4221 Quantum Mechanics I (Fall 2004) Quiz 4...

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Unformatted text preview: PHY4221 Quantum Mechanics I (Fall 2004) Quiz 4 (Answers) Since n is the normalized n th eigen-function of this system, so we have that: ( 29 2 cos 1,3,5, 2 2 sin 2,4,6, 2 n n x n L L L x n x x n L L L x = = = (1) Thus we know that at time t =0, the wave function of this particle is: ( 29 ( 29 ( 29 1 3 2 3 ,0 3 3 cos cos x x x x x L L L = + = + (2) Then, with the propagator we could construct the wave function at any time: ( 29 ( 29 ( 29 , , ; ,0 ,0 x t dx K x t x x - = (3) In equation (3), we have the definition of the propagator as following: ( 29 ( 29 ( 29 , ; ,0 exp n n n n E t K x t x x x i =- h (4) So finally we get: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 /2 / 2 /2 /2 /2 1 3 /2 1 , exp ,0 exp ,0 exp...
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This note was uploaded on 12/10/2011 for the course PHYS 4221 taught by Professor Cflo during the Spring '11 term at CUHK.

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4thQuiz - PHY4221 Quantum Mechanics I (Fall 2004) Quiz 4...

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