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Unformatted text preview: Georg.Hoffstaetter@Cornell.edu 57 02/28/2005 Time dependence of quantum states = - t i n n E e x t x ) ( ) , ( Stationary states satisfy the time independent Schrdinger equation. The probability distribution is constant in time: and can therefore not describe moving particles 2 2 ) ( x = A linear combination of stationary states satisfies the time dependent Schrdinger equation and leads to time dependent probability distributions: ] Re[ 2 | | | | .) . ( | | | | ) )( ( | | ) ( ) ( ) , ( * 2 2 * 2 2 * * 2 t i m n m n t i m n m n t i m t i n t i m t i n t i m t i n m E n E m E n E m E n E m E n E m E n E e C C e e e e e e x e x t x -- + + = + + + = + + = + = ---- ) ( ) ( ) ( ) ( 2 2 2 2 x E x x V x x m = + - Georg.Hoffstaetter@Cornell.edu 58 02/28/2005 Time dependent states in an infinite well t i t i E E e x A e x t x 1 ) ( ) ( ) , ( 1 1-- + =- = 8 )...
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell University (Engineering School).
- Spring '05