Evaluating Harmonic Oscillator Propagator with Stochastic Decoupling
By virtue of stochastic decoupling,the quantum evolution of a harmonic oscillator is convert-ed into two virtual contributions dictated by either a stochastic creation operator or a stochastic annihilation operator.Two approaches are provided to resolve these virtual two evolution operators.One is based on the coherent-state representation and the other deals with the momentum representation after separating out the position and momentum factors.The quantum propagator of the harmonic oscillator is obtained by taking the random aver-age of the combined virtual propagators.The main mathematical exercise of the whole proce-dure is the calculation of the Gaussian integral.
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