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Mathematics 2015, 3(2), 319-328; doi:10.3390/math3020319

There Are Quantum Jumps

Department of Chemistry, Ångström Laboratory, Institute of Theoretical Chemistry, Uppsala University, P.O. Box 518, S-751 20 Uppsala, Sweden
Academic Editor: Palle E.T. Jorgensen
Received: 10 March 2015 / Accepted: 20 April 2015 / Published: 5 May 2015
(This article belongs to the Special Issue Mathematical physics)
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Abstract

In this communication we take up the age-old problem of the possibility to incorporate quantum jumps. Unusually, we investigate quantum jumps in an extended quantum setting, but one of rigorous mathematical significance. The general background for this formulation originates in the Balslev-Combes theorem for dilatation analytic Hamiltonians and associated complex symmetric representations. The actual jump is mapped into a Jordan block of order two and a detailed derivation is discussed for the case of the emission of a photon by an atom. The result can be easily reassigned to analogous cases as well as generalized to Segrè characteristics of arbitrary order. View Full-Text
Keywords: dilation analytic family of operators; complex symmetric representation; Segrè characteristic; Jordan block dilation analytic family of operators; complex symmetric representation; Segrè characteristic; Jordan block
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Brändas, E.J. There Are Quantum Jumps. Mathematics 2015, 3, 319-328.

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