A. Streclas

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.

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.

Some Properties of Commutators and the Equations of Motion

In this paper we calculate the commutators of operator functions for non-commuting operators on a Heisenberg ring. The commutator of two operators can be expressed with the help of the fundamental operators and their differentials. Using the theorem of the derivative of a function of operators with respect to any parameter, we can find tne equation of motion of a system, in canonical and non-canonical quantum mechanics.

Boltzmann statistics of quantum friction

Abstract In this paper we investigate the thermodynamic properties of simple quantum-mechanical systems in the presence of friction. Using the propagators for these simple models we calculate the response functions in Boltzmann statics. In the low temperature region the response functions exhibit singular behaviour.

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