N. Patargias

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.

Ordering of the Exponential of Quadratic Forms in Boson Operators and Some Applications

In the present paper we order operators of the general form exp [αa2 + βa+2 + γ(a+a + aa+) + δa + a+], using parametric differentiation. Using this ordered form we derive the density matrices and the canonical Wigner distribution function of the harmonic oscillator and of the electromagnetic field in a simple straightforward manner.

Generalized Coherent States and the U (n) Lie Group

In this paper we study the generalized coherent states (g.c.s.) in n -dimensional space. Their annihilation operators consist of linear combinations of the annihilation operators a l , and their coherent states are the product of the simple coherent states. All the known annihilation operators which have been studied as yet, and also the magnetic ones, are special cases of these operators. The new operators A k + A m form the Lie algebra U ( n ) of the Lie group U ( n ). Finally, instead of the operators a l and a l + we can use the new operators, which depend on a complex parameter.

Two-photon Jaynes–Cummings model in Kerr-like media

In the present paper are found the solution of a model-Hamiltonian that describes the three-level two cavity mode Jaynes–Cummings model in Kerr-like media (nondegenerate case). Finally we calculate atom level populations as well as squeezing for the quadrature components of the cavity modes and of the total field.

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.

Electrodynamics of a three-level Jaynes-Cummings model in a Kerr-like medium

In this paper we study the dynamics of a three level Jaynes-Cummings model (J-C model) interacting with a Kerr-like medium. We examine the influence of the Kerr medium coupling in the time evolution of the level population as well as in the squeezing phenomenon which is found to be stronger.

Wigner operators of angular momentum in phase space

Two kinds of Wigner operators are presented. The first kind is the sum of the ordinary angular-momentum operators in p and q representations and the second is a new kind. These operators can be derived from the usual angular-momentum operators by the help of Wigner representation in phase space. For the components of the angular-momentum operators of a particle we have the expressions (1) LI = q2P3 qaP~ , L2 = q3Pl qlP3 , L3 = q x P B q~Pl , where the following rules held (2) [•i, L~] = i ~ e i ~ L k , i , j , Iv = 1, 2, 3 . We substitute in (1) the Bopp-Kubo (1,~) operators for q~ ,p~ and we have