No abstract available

[en] Short communication

[en] The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as was explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory. Separate abstracts have been prepared for items from this conference

[en] A realization of the Heisenberg q-algebra whose generators are first-order difference operators on the full real line is discussed. The eigenfunctions of the corresponding q-oscillator Hamiltonian are given explicitly in terms of the q^-1 Hermite polynomials. The non-uniqueness of the measure for these q-oscillator is also studied. 15 refs

[en] This volume gives a broad overview of symmetry methods applied to molecular and nuclear physics, particle physics, decay processes, and phase space dynamics. The thoroughly edited contributions should be of interest not only to scientists but also to all those wanting to see how symmetry considerations are put to work in twentieth century physics. (orig.)

[en] Gaussian beams that include a set of phase functions having a purely quantum mechanical analog are examined; these are coherent states, correlated and discrete modes for quantum oscillators that model optical fibers. In propagating through free space these beams lose coherence and aberrations appear. The authors describe these aberrations and investigate such observables as the beam center, the beam width and the evolution of the correlation coefficient. This is done for systems described by optical models having a Hamiltonian that is an arbitrary function of the momentum expanded into a series and diverging in a certain region including the optical axis. The paraxial approximation is investigated in detail as a particular case of accounting for only the first term in the expansion

No abstract available

[en] The squeezed states used in optics are a mathematical approximation from quantum mechanics. Monochromatic electromagnetic fields obey the Hemholtz equation, of which the Schrodinger equation is the paraxial approximation. We define solutions of the Helmholtz equation that contain them in that limit. (Author) 11 refs

[en] The definition of the polarization for the quantum harmonic oscillator system is analysed in a group-theoretical scheme. (orig.)

[en] We consider a new Lie-algebraic framework for the Poeschl-Teller potential, in which a single [sp(2,r) Casimir] operator has both bound and scattering states. This approach allows the determination of the S matrix by purely algebraic means