Monte Carlo Hamiltonian: Inverse Potential

TL;DR

This paper introduces an improved Monte Carlo Hamiltonian approach for inverse potentials, utilizing effective potential and extrapolation techniques to better analyze quantum systems like hydrogen.

Contribution

It proposes a novel method combining effective potential and extrapolation to address challenges in Monte Carlo simulations of inverse potentials.

Findings

Successfully applied to hydrogen system examples.

Enhanced accuracy in low-lying state calculations.

Overcomes limitations of conventional Monte Carlo methods.

Abstract

The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some difficulties when applying to inverse potentials. We propose to use effective potential and extrapolation method to solve the problem. We present examples from the hydrogen system.