Non-Hermitian quantum mechanics

I. Gilary, A. Fleischer, N. Moiseyev, Calculations of time-dependent observables in non-Hermitian quantum mechanics The problem and a possible solution, Phys. Rev. A 72 (2005) 012117/1. 

N. Moiseyev, Non-Hermitian Quantum Mechanics, Cambridge University Press, Cambridge, UK, 2011. 

NON-HERMITIAN QUANTUM MECHANICS THEORY AND EXPERIMENTS NOT AMENABLE TO CONVENTIONAL QM... 

Recently there is a growing interest in non Hermitian quantum mechanics. Non Hermitian (NH) quantum mechanical (QM) formalism is being used to study and explain physical phenomena. Sharp structures in elec-tron/molecule collision cross sections and abrupt change of the phase of the transition probability amplitude associated with an electron traversing quantum dot are only a few of many examples. 

Physical phenomena explained by non Hermitian quantum mechanics... 

We have used non-Hermitian scattering theory to calculate the transition probability amphtude, within the framework of the complex adiabatic approach. It should be stressed that non-Hermitian quantum mechanics allows us to use complex adiabatic potential energy surfaces in cases where one has to go beyond the adiabatic approximation in Hermitian quantum mechanics [1,2]. In the adiabatic approximation, we assume that the motion in the y direction is much slower than in the x direction. This assumption is based on the geometry of the two-dimensional potential surface (see Fig. 5). 

In this work we show how the complex adiabatic approach developed within the framework of the non-hermitian quantum mechanics, enables the study of dynamics of systems which is hard and even impossible to study by the use of the conventional (hermitian) QM. We focused here on two phenomena which have been observed in two different experiments. The first one is... 

Non-Hermitian quantum mechanics Theory and experiments not amenable to conventional QM 311... 

Moiseyev N (2011) Non-Hermitian quantum mechanics. Cambridge University Press,... 

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