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Unformatted text preview: q cl ( t ) = 0 when j ( t ) = 0. When solving classical EOM you may nd Fourier-integral decomposition q ( t ) = i- dE 2 e-i h E t q E useful. b. (10 pts) Use the result of part a to show that the two-point 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 e-i h E ( t 1-t 2 ) E 2 h 2 2 + i . (1) 1 c. (10 pts) Re-derive the two-point 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 e-i 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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