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

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

2011-01-20

arxiv.org/abs/1101.3969v1

Physics

Quantum Physics

This paper presents a mathematically rigorous reworking of some of the results appearing in arXiv:0802.2448 [quant-ph]

Scientific paper

In [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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