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Unformatted text preview: q cl ( t ) = 0 when j ( t ) = 0. When solving classical EOM you may nd Fourierintegral decomposition q ( t ) = i dE 2 ei h E t q E useful. b. (10 pts) Use the result of part a to show that the twopoint function for the harmonic oscillator without the external force is given by a  T q ( t 1 ) q ( t 2 )  A = i h 2 m i dE 2 ei h E ( t 1t 2 ) E 2 h 2 2 + i . (1) 1 c. (10 pts) Rederive the twopoint function in Eq. (1) by using creation and annihilation operators. For the simple harmonic oscillator (without the external force) write q ( t ) = r h 2 m b a ei t + a e i t B and use commutation relations for a and a ([ a, a ] = 1, all other commutators are zero) to obtain Eq. (1). 2...
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This note was uploaded on 07/28/2011 for the course PHYSICS 880.08 taught by Professor Staff during the Fall '10 term at Ohio State.
 Fall '10
 Staff
 Work, Quantum Field Theory

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