Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics

Yossef Strauss, Jonathan Silman, Shai Machnes, Lawrence P. Horwitz

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

In [Y. Strauss, Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schrödinger evolution, J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its expectation value decreases monotonically for any initial state. In this paper we study some of this operator's properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.

Original languageEnglish
Pages (from-to)1117-1122
Number of pages6
JournalComptes Rendus Mathematique
Volume349
Issue number19-20
DOIs
StatePublished - 1 Nov 2011
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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