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Synthesis lectures on mathematics and statistics

Variational Monte Carlo Method Applied to the Ground State of a Simple Harmonic Oscillator

Sujaul Chowdhury

Published Jan 1, 2021• 0 citations
Publisher
DOI
10.1007/978-3-031-02429-0_3

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We present a variational Monte Carlo (VMC) method that works equally well for the ground and the excited states of a quantum system. The method is based on the minimization of the variance of energy, as opposed to the energy itself in standard methods. As a test, it is applied to the investigation of the universal spectrum at the van der Waals length scale for two identical Bose atoms in a symmetric harmonic trap, with results compared to the basically exact results obtained from a multiscale quantum-defect theory.