Mathematical Physics
Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1117-1122.

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 operatorʼs properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.

Dans [Y. Strauss, Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schrödinger evolution, J. Math. Phys. 51 (2010) 022104], un opérateur auto-adjoint a été introduit ayant la propriété dʼindiquer la direction du temps dans le formalisme standard de la mécanique quantique, au sens où sa valeur moyenne décroit de façon monotone avec le temps pour tout état initial. Dans cet article, nous étudions les propriétés de cet opérateur. En particulier, nous dérivons son spectre et ses vecteurs propres généralisés et traitons en détail lʼexample de la particule libre

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DOI: 10.1016/j.crma.2011.09.007
Strauss, Yossef 1; Silman, Jonathan 2; Machnes, Shai 2; Horwitz, Lawrence P. 2, 3, 4

1 Einstein Institute of Mathematics, Edmond J. Safra campus, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
2 School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
3 Physics Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
4 Department of Physics, The Ariel University Center of Samaria, Ariel 40700, Israel
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Strauss, Yossef; Silman, Jonathan; Machnes, Shai; Horwitz, Lawrence P. Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1117-1122. doi : 10.1016/j.crma.2011.09.007. http://www.numdam.org/articles/10.1016/j.crma.2011.09.007/

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