Discrete Time Quantum Mechanics

Document Type

Article

Publication Date

11-1-1994

Department

Computing

School

Computing Sciences and Computer Engineering

Abstract

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy based on the method of finite elements. We are able to formulate fully consistent quantum-mechanical systems directly on a lattice in terms of operator difference equations. One advantage of this discretized formulation of quantum mechanics is that the ambiguities associated with operator ordering are eliminated. Furthermore, the scheme provides an easy way in which to obtain the energy levels of the theory numerically. A generalized version of this discretization scheme can be applied to quantum field theory problems. The difficulties normally associated with fermion doubling are eliminated. Also, one can incorporate local gauge invariance in the finite-element formulation. Results for some field theory models are summarized. In particular, we review the calculation of the anomaly in two-dimensional quantum electrodynamics (the Schwinger model). Finally, we discuss nonabelian gauge theories.

Publication Title

Computers & Mathematics with Applications

Volume

28

Issue

41559

First Page

279

Last Page

317

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