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Unformatted text preview: FREE PARTICLES 1 I: Onedimensional wave functions A. Free particle with momentum p : 1. Write down the de Broglie relations relating momentum ( ~ p ) to wavelength ( ) and energy to frequency. Momentum is a vector but wavelength is not. How do you reconcile this discrepancy? 2. Physicists tend to introduce new terms in order to simplify working with equations. To day, we will use the following terms: ~ k = (2 / ) r : wave vector where r is the direction of propagation of the wave = 2 f : angular frequency ( f is the frequency of a wave) ~ = h/ (2 pi ): A convenient term (pronounced h bar) which helps keep track of many of the factors of 2 which appear in quantum mechanics Write the deBroglie relations using the wave vector, the angular frequency, and ~ . 3. What is the general form in one dimension of the wave function for a free particle of mass m and momentum p ? Recall that the wave function has to satisfy the onedimensional Schr odinger equation: i ~...
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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.
 Fall '08
 STEVEPOLLOCK
 Energy, Momentum

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