The Howland-Kato Commutator Problem II

TL;DR

This paper investigates conditions under which the commutator of certain bounded functions of position and momentum operators is a finite rank, non-negative operator, extending previous work on the Howland-Kato problem.

Contribution

It advances understanding of the Howland-Kato commutator problem by analyzing cases where the commutator is a finite rank operator.

Findings

Identifies conditions for non-negative finite rank commutators

Provides new characterizations of functions f and g

Extends previous theoretical results on operator commutators

Abstract

We continue to discuss the following problem: For which bounded measurable real functions f and g is the commutator i[f(P),g(Q)] a non-negative operator on L^2(R)? In this work we concentrate on the situation where the commutator is a finite rank operator.