Some Comments on the RHS Formulation of Resonance Scattering

We discuss the validity of a relation betweenfunctionals in quantum resonance scattering which isoften used in the current literature.     

General Properties of the Liouville Operator

We study the self-adjointness of the Liouvillianof a symmetric operator. We also discuss some cases ofthe spectrum of the Liouville operator of a self-adjointHamiltonian with purely continuous singular spectrum. The presence of an absolutelycontinuous part for the spectrum of Liouvillianscorresponding to Hamiltonians with purely continuoussingular spectrum shows that quantum theory in Hilbertand Liouville spaces is not equivalent.     

On the Mathematical Basis of the Dirac Formulation of Quantum Mechanics

We discuss various attempts to implement mathematically the Dirac formulation of Quantum Mechanics. A first attempt used Hilbert space. This formalization realizes the Dirac formalism if and only if the spectra of the observables under consideration is purely discrete. Therefore, generalized spectral decompositions are needed. These spectral decompositions can be constructed in the framework of rigged Hilbert spaces. We construct generalized spectral decompositions for self-adjoint operators using their spectral measures. We review the previous work by Marlow (in Hilbert spaces), Antoine, Roberts, and Melsheimer and complete it. We show that these generalized spectral decompositions fit well in the framework of a theory constructed by Kato and Kuroda and that all the results can be reproduced in this framework.     

Time-Reversal, Irreversibility and Arrow of Time in Quantum Mechanics

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect of its validity as a non time-reversal invariant, time-asymmetric theory as well as of its ability to determine an arrow of time.     

A Study of Resonances in a One-Dimensional Model with Singular Hamiltonian and Mass Jumps

We study the resonances produced in a one dimensional quantum system with an infinite potential on the negative real line plus two Dirac delta barriers centered at the points a,b>0. The system mass is not constant but undergoes jumps at the singular points a and b of the potential. We study the behavior of the resonances under the change of parameters such that the weight of the deltas or the heights of mass jumps. Possible degeneration of these resonances is also considered.     

Quantization on a two-dimensional phase space with a constant curvature tensor

Some properties of the star product of the Weyl type (i.e., associated with the Weyl ordering) are proved. Fedosov construction of the *-product on a two-dimensional phase space with a constant curvature tensor is presented. Eigenvalue equations for momentum p and position q on a two-dimensional phase space with constant curvature tensors are solved.