A. Leodaris

Non-Hermitian realization of a Lie-deformed Heisenberg algebra

We discuss the non-Hermitian realization of a Lie-deformed, non-canonical Heisenberg algebra. We show that it essentially amounts to the case of a Q-deformed algebra with complex deformation parameter. The (real) energy eigenvalues of the corresponding oscillator are derived, whose deformed spectrum has, among the others, a ground state energy lower than that of the usual harmonic oscillator. The non-Hermitian deformed SU(2) algebra is also constructed.

Heisenberg equations of motion in the Caldirola-Montaldi procedure

SummaryIn this paper the procedure of Caldirola and Montaldi is applied in the Heisenberg representation. It is also proved here that the introduction of the parameter τ contributes to the specification of a quantum-dissipative system, as exactly happens in the Schrödinger representation. As an example the case of the harmonic oscillator as well as that of the damped harmonic oscillator are examined.RiassuntoIn questo lavoro si applica la procedura di Caldirola e Montaldi nella rappresentazione di Heisenberg. Si prova che l’introduzione del parametro τ contribuisce alla specificazione di un sistema quantodissipativo, esattamente come accade nella rappresentazione di Schrödinger. Si esaminano come esempi il caso dell’oscillatore armonico e quello dell’oscillatore armonico smorzato.РезюмеВ этой статье процедура Калдиролы-Монтальди применяется в представлении Гайзенберга. Доказывается, что параметр τ приводит к спецификации квантовой диссипативной системы, аналогично рассмотрению в представлении Шредингера. Как пример, исследуется случай гармонического осциллятора, а также случай затухающего гармонического осциллятора.

Non-Hermitian harmonic oscillator with discrete complex or real spectrum for non-unitary squeeze operators

In the present paper, we enlarge the method of Debergh, Beckers and Szafraniec for non-Hermitian Hamiltonians with complex parameters and obtain real eigenvalues. For the case of non-unitary squeeze operators with two complex parameters of non-Hermitian harmonic oscillator, we obtain discrete complex spectrum and for special values of the complex parameters, the spectrum is discrete real and positive even though the corresponding operators are not PT symmetric.

Quantum friction in a periodic potential

In this paper we study the quantum friction problem using the Hamiltonian of Caldirola-Kanai for a periodic Mathieus type potential. In the sequel we study the lattice electron with friction we introduce a new effective Hamiltonian of the Caldirola-Kanai form for a Blochs band. Finally we study the cases of closed solutions of Schrodingers equation.

Study of the Stark and Zeeman effects in parabolic coordinates

Abstract By means of perturbation theory and using parabolic coordinates we calculate the energy eigenvalues of the hydrogen atom in external uniform electric and magnetic fields, both parallel to the z -axis.