Quantum mechanics in a cut Fock space

TL;DR

This paper analyzes a numerical method for quantum systems using a truncated Fock space basis, proving convergence and deriving a new scaling law for nonlocalized states, with exact solutions and general properties discussed.

Contribution

It introduces a new scaling law for nonlocalized states in a truncated Fock space approach to quantum systems, with proofs of convergence and exact solutions provided.

Findings

Proved convergence of the truncated Fock space method.

Derived a new scaling law for nonlocalized states.

Provided exact solutions for specific cases.

Abstract

A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between discrete and continuous spectrum is stressed. In particular a new scaling low for nonlocalized states is obtained. Exact solutions for several cases as well as general properties of the method are given.