Variational Quantum Monte Carlo Method: A pedagogical approach

Abstract

We present a report that describes the stochastic variational Monte Carlo method underlying ideas and techniques, such as the Metropolis Algorithm in a multi-dimensional space. We design Fortran codes that generates, according to Metropolis, random numbers with non-uniform density, to sample local energy and its squared. Then, we compute energy and energy squared as the average of their local partners and, from them, the variance. We enclose illustrative calculations on the Harmonic Oscillator, Hydrogen atom and Helium atom ground states.