TY - JOUR

T1 - Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics

AU - Strauss, Yossef

AU - Silman, Jonathan

AU - Machnes, Shai

AU - Horwitz, Lawrence P.

N1 - 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.

PY - 2011/11

Y1 - 2011/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80054012818&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2011.09.007

DO - 10.1016/j.crma.2011.09.007

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AN - SCOPUS:80054012818

SN - 1631-073X

VL - 349

SP - 1117

EP - 1122

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 19-20

ER -