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理论物理通讯：英文版

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

Luo, Xiang-Qian, Xu, Hao, Yang, Jie-Chao, Chang, Di, Lin -, Yin, Helmut, Kroger, Wang, Yuli

Published Jan 1, 2001• 1 citation
OpenAlex

Abstract

In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora 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 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.``

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In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora 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 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.``
Monte Carlo Hamiltonian method is a new algorithm for numerical simulation of quantum theories. The advantage is its ability to study spectrum and wave functions beyond the ground state. The previous approach needs information on free particles and is difficult to be used for lattice gauge theory. In this paper, we propose a new approach to MCH, which may overcome the difficulty. We describe the basic ideas, and use a 1-dimensional quantum mechanical model V(x) =μ2x2 + λx4(with μ2 0,λ 0) as an example.