In the present paper, we have extended the usual uncertainty relations, as well as the entropic uncertainty relations to the mixed states, particularly to the thermal states, using the density matrix formalism. As quantum model we have choosen the quantum mechanical ideal gas with the harmonic oscillator-like Hamiltonian H_lambda introduced by Beckers, Debergh and Szafraniec, generically named BDS-Hamiltonian.

In the paper we have investigated some properties of the Barut–Giraradello coherent states (BGCS) (the eigenstates of the SU(1, 1) lowering generator K− for the Hamiltonian of the pseudoharmonic oscillator (PHO). By using these states, the diagonal P-representation of the density operator is constructed as a new result for this potential. In addition, we have calculated some thermal expectation values for the quantum canonical gas of the PHOs.

In the paper we construct a new set of coherent states for a deformed Hamiltonian of the harmonic oscillator, previously introduced by Beckers, Debergh, and Szafraniec, which we have called the BDS-Hamiltonian. This Hamiltonian depends on the new creation operator, i.e. the usual creation operator displaced with the real quantity lambda. In order to construct the coherent states, we use a new measure in the Hilbert space of the Hamiltonian eigenstates,

In a previous paper (Popov D 2001 J. Phys. A: Math. Gen. 34 5283) we have constructed the coherent states (CSs) of the pseudoharmonic oscillator (PHO). These states are of the Barut-Girardello type. In the present paper, we have constructed and investigated some properties of the photon-added Barut-Girardello coherent states (PA-BGCSs) of the PHO. These states are not orthogonal but are normalized and satisfy a unity resolution relation (the completeness

The dispersion law and spectral weights of electrons in perturbed thin film structures with two sublattices was derived by the method of two-time, single-electron Green's functions. In variance from simple cubic structure, electron energy zone splits into two allowed energy bands and forbidden energy gap appears. In contrast to continual energy zone of allowed electron states in bulk crystals, the energy spectra in ultrathin films are discrete. The

Thermal conductivity of thin lm is analyzed in this paper. It has been shown that at low temperatures, thermal conductivity of lm is considerably lower than that of bulk structure. Also, the dependence of activation energy on boundary conditions has been investigated. It has been found that the implantation of light molecules in lm boundaries leads to considerably higher activation temperatures. Our theoretical results proved to be in agreement with

We generalize the Dirac equation to D+1 space–time. The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momentums are calculated for both odd D and even D cases. The exact solutions of the D+1-dimensional radial equations of the Dirac equation with a Coulomb plus scalar potential are analytically presented by studying the Tricomi equations obtained from a pair of coupled first-order

Using the Klauder-Perelomov coherent states of the pseudoharmonic oscillator Hamiltonian, corresponding diagonal P-representation for the density matrix of the gas of pseudoharmonic oscillators in thermal equilibrium is constructed. With a help of this new result, some corresponding characteristic thermal expectation values are obtained.

The comprehesive conditions concerning the harmonic limit of the Morse oscillator are investigated in this paper. These conditions extend the over-simple "classical" condition, which results by truncating the expansion of the Morse potential function in the power series of the coordinate close to the equilibrium position. The validity of the obtained results is tested by calculating the harmonic limit of the expected values of some characteristic

We present in this paper a realistic construction of the coherent states for the Morse potential using the Klauder-Perelomov approach. We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated.