A. Jannussis

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.

Coherent states for the harmonic oscillator with time-dependent mass and frequency

Abstract Exact coherent states for the harmonic oscillator with time-dependent mass and frequency are constructed. Interesting is the case of a damped harmonic oscillator. The new coherent states result exactly as partial cases of the coherent states of Yuen which are equivalent to the well-known squeezed states.

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.

Dissipative tunnelling of the inverted Caldirola-Kanai oscillator

We discuss, in the phase time approach, quantum tunnelling in the presence of dissipation for an inverted oscillator with Caldirola-Kanai damping. The exact expressions of time delay, traversal time and effective tunnelling velocity are derived. Some paradoxical aspects of tunnelling related to the particle speed in crossing the barrier-such as the Hartmann-Fletcher effect-are briefly considered.

New deformed Heisenberg oscillator

The discrete spectrum of a deformed oscillator is calculated here for the first time according to the noncanonical Heisenberg algebra. The spectrum extends from omega /2(1+ mu ) to omega / mu , where mu is a positive deformation parameter.

Exact calculation of the squeezed states in the q-representation

Abstract In the present note by using a scale transformation we find that the squeeze operator is proportional to the well-known multiplication operator and from which we obtain the exact squeezed states function of single- and two-mode squeeze operators in the q -representation.

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.

Eigenfunctions and eigenvalues of the Wigner operator

Abstract It can be proved, that the Wigner operator, which results from the Quantum-Mechanical foundation of Bopp, accepts as eigenvalues the differences of the eigenvalues of two equivalent Schrodinger equations. The eigenfunctions result with the help of a Fourier transform in the phase space of the corresponding eigenfunctions of the Schrodinger equations.

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.