G. Brodimas

Propagator with friction in quantum mechanics

Abstract In this paper we calculate the propagator for quantum-mechanical systems with friction. For the case where the friction is a linear function of the velocity with a friction constant γ we can calculate exact propagators of quadratic form.

Bose realization of a non-canonical Heisenberg algebra

The authors find out the Bose realization of a generalized Heisenberg algebra, in which the bracket of the annihilation and creation operators is proportional to a polynomial function of the number operator. The eigenvalues of the corresponding oscillator are derived in a special case. They stress also the connection between non-canonical commutation relations and q-algebras.

Quantum groups and Lie-admissible time evolution

The time evolution of operators for q-oscillators is derived for the first time by exploiting the connection between q-deformation algebras and Lie-admissible algebras.

New Creation and Annihilation Operators in Phase Space

New creation and annihilation operators of the harmonic oscillator in the phase space are considered. The common base of these operators is a generalized Wigner distribution and their coherent states are determined. Using these operators Weyls displacement operators and Bopps translation operators are also determined.

New creation and annihilation operators in the Gauss plane and quantum friction

Abstract We construct new creation and annihilation operators in the Gauss plane depending on a parameter, the imaginary part of which describes dissipative phenomena while the real part describes rotations.

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.

Effective Hamiltonian for Bloch-electrons in uniform electric and magnetic fields

Abstract It is possible to generalize the Peierls-Luttinger theorem for a Bloch electron in a uniform electric and magnetic field, by using an appropriate exponential transformation.

Generalized coherent states

On cherche des etats coherents generaux basee sur la methode de factorisation de Infeld et Hull

ANNIHILATION AND CREATION OPERATORS FOR THE CALDIROLA–KANAI HAMILTONIAN WITH COMPLEX FRICTION COEFFICIENT

In the present note, we consider the annihilation and creation operators with complex friction coefficient and we find the coherent, squeezed states, the uncertainty Heisenberg relation and the behavior of the PT and, CPT symmetries. Also we demonstrated that the (CK) Hamiltonian is a special case of the complex time-dependent mass.

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.