On a few new quantization recipes using $$\mathcal{P}\mathcal{T}$$ -symmetry

Abstract

A review of a few recent developments in our analysis and applications of the coupledchannel version of the formalism of PT -symmetric quantum mechanics is given.

A non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations

“…This completes the extension of [9] to the whole family of generalized non-Hermitian oscillator Hamiltonians, defined in (2).…”

“…(3), reduces to that considered in [9]. Since, however, the validity of our new derivation is independent of the chosen realization, it applies to other Hamiltonians satisfying equation (2). In the second part of this paper, we will provide some examples of such Hamiltonians, which may be called 'generalized non-Hermitian oscillator Hamiltonians'.…”

“…Non-Hermitian Hamiltonians H with a real spectrum are currently an active field of research, motivated both by the necessity to understand their mathematical properties and by the requirement to build a consistent unitary theory of quantum mechanics for them (see [1,2] for recent surveys). and is termed quasi-Hermitian [3].…”

Thermodynamics of Pseudo-Hermitian Systems in Equilibrium

“…[9,10]). This idea initiated an intensive study of pseudo-hermitian operators with anti-linear symmetries [11,12,13,14,15] where the original specific choice of the parity is being extended to any invertible hermitian mapping η such that the operator equation…”

“…However, let us pretend that the spectrum of the operator is hard to be found. We shall solve the equation (14). Separating the Hamiltonian into its hermitian part and nonhermitian perturbation term…”