Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics
arXiv:1101.3969 · doi:10.1016/j.crma.2011.09.007
Abstract
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.
This paper presents a mathematically rigorous reworking of some of the results appearing in arXiv:0802.2448 [quant-ph]