sp02mod_sol

sp02mod_sol - PHY6938 Proficiency Exam Spring 2002 April 5,...

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Unformatted text preview: PHY6938 Proficiency Exam Spring 2002 April 5, 2002 Modern Physics and Quantum Mechanics 1. Consider the Schr odinger equation for the linear harmonic oscillator,- h 2 2 m d 2 dx 2 + 1 2 m 2 x 2 = E , where m is the mass of the particle and is the angular frequency. The wavefunction and energy of the ground and first excited state are given by GS ( x ) = s exp(- 2 x 2 / 2) , E GS = 1 2 h E 1 ( x ) = s 2 2 x exp(- 2 x 2 / 2) , E E 1 = 3 2 h , respectively, where = q m/ h . A perturbation term H =- m 2 xx is added to the Hamiltonian of the harmonic oscillator. The following integral may be useful: Z - dx x 2 exp(- x 2 ) = / 2 (a) Calculate the transition matrix element h GS | H | E 1 i . h GS | H | E 1 i =- m 2 x 2 s 2 Z - dx x 2 exp h- 2 x 2 i = [change variable, x = x ] =- m 2 x s 2 1 Z - dx x 2 exp h- x 2 i =- m 2 x s 2 1 2 =- m 2 x 1 2...
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This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.

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sp02mod_sol - PHY6938 Proficiency Exam Spring 2002 April 5,...

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