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Communications in Theoretical Physics

(3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator

Luo Xiangqian, Hao Xu, Yang Jie-Chao, Yuli Wang, Chang Di, Lin Yin, H. Kröger

Published Jul 15, 2001• 4 citations
Publisher

Abstract

In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions of a quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1+1 and 2+1 dimensions. In this paper we apply it to the study of the low-energy quantum physics of the (3+1)-dimensional harmonic oscillator.

DOI
10.1088/0253-6102/36/1/7

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Monte Carlo techniques with importance sampling have been extensively applied to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is extremely difficult to compute the excited states using the conventional Monte Carlo algorithm. Our recently developed approach: the Monte Carlo Hamiltonian method, has been designed to overcome the difficulties of the conventional approach. In this paper, we extend the method to many body systems and quantum field theory. The Klein-Gordon field theory is used as a testing ground.