Underlying non-Hermitian character of the Born rule in open quantum systems

Abstract

The absolute value squared of the probability amplitude corresponding to the overlap of an initial state with a continuum wave solution to the Schrödinger equation of the problem, has the physical interpretation provided by the Born rule. Here, it is shown that for an open quantum system, the above probability may be written in an exact analytical fashion as an expansion in terms of the non-Hermitian resonance (quasinormal) states and complex poles to the problem which provides an underlying non-Hermitian character of the Born rule.

arXiv comment8 pages, 2 figures

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Cited by in corpus (2)

• Numerical calculation of the decay widths, the decay constants, and the decay energy spectra of the resonances of the delta-shell potential
• Heisenberg uncertainty relations for the non-Hermitian resonance state solutions to the Schrödinger equation