Faria, C. F. D. M. & Fring, A. (2007). NonHermitian Hamiltonians with real eigenvalues coupled to electric fields: From the timeindependent to the timedependent quantum mechanical formulation. Laser Physics, 17(4), pp. 424437. doi: 10.1134/S1054660X07040196

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Abstract
We provide a reviewlike introduction to the quantum mechanical formalism related to nonHermitian Hamiltonian systems with real eigenvalues. Starting with the timeindependent framework, we explain how to determine an appropriate domain of a nonHermitian Hamiltonian and pay particular attention to the role played by PJ symmetry and pseudoHermiticity. We discuss the time evolution of such systems having in particular the question in mind of how to couple consistently an electric field to pseudoHermitian Hamiltonians. We illustrate the general formalism with three explicit examples: (i) the generalized Swanson Hamiltonians, which constitute nonHermitian extensions of anharmonic oscillators, (ii) the spiked harmonic oscillator, which exhibits explicit supersymmetry, and (iii) the −x 4potential, which serves as a toy model for the quantum field theoretical ϕ4theory.
Item Type:  Article 

Uncontrolled Keywords:  PTSYMMETRY, PSEUDOHERMITICITY, MOYAL PRODUCTS, POTENTIALS, SPECTRUM, STABILIZATION, OSCILLATORS, IONIZATION, OPERATORS, EQUATIONS 
Subjects:  Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/696 
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