Reply to Comment by Galapon on 'Almost-periodic time observables for bound quantum systems'

TL;DR

This paper critically examines Galapon's proposed Hermitian time operator, clarifying certain mathematical aspects and emphasizing that the operator's applicability is limited to a measure-zero set of times in quantum systems.

Contribution

The paper refines the critique of Galapon's time operator, addressing domain issues and clarifying its limited applicability in quantum systems.

Findings

Galapon's denseness remarks are correct.

The time operator applies only at measure-zero times.

The critique clarifies the operator's limitations.

Abstract

In a recent paper [1] (also at http://lanl.arxiv.org/abs/0803.3721), I made several critical remarks on a 'Hermitian time operator' proposed by Galapon [2] (also at http://lanl.arxiv.org/abs/quant-ph/0111061). Galapon has correctly pointed out that remarks pertaining to 'denseness' of the commutator domain are wrong [3]. However, the other remarks still apply, and it is further noted that a given quantum system can be a member of this domain only at a set of times of total measure zero.