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

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

doi:10.1016/j.crma.2011.09.007

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

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

Department of Physics

Research output: Contribution to journal › Article › peer-review

9 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 language	English
Pages (from-to)	1117-1122
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	349
Issue number	19-20
DOIs	https://doi.org/10.1016/j.crma.2011.09.007
State	Published - Nov 2011

Bibliographical note

Funding Information:
Y.S. acknowledges the support of the Israeli Science Foundation Grants no. 1169/06 and 1105/10, and the Center for Advanced Studies in Mathematics at Ben-Gurion University, where part of this research was conducted. J.S. and S.M. acknowledge the support of the Israeli Science Foundation Grant no. 784/06.

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10.1016/j.crma.2011.09.007

http://www.numdam.org/item/10.1016/j.crma.2011.09.007.pdf

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title = "Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics",

abstract = "In [Y. Strauss, Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schr{\"o}dinger 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.",

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

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