Coherent States for Generalized Laguerre Functions

We explicitly construct a Hamiltonian whose exact eigenfunctions are the generalized Laguerre functions. Moreover, we present the related raising and lowering operators. We investigate the corresponding coherent states by adopting the Gazeau-Klauder approach, where resolution of unity and overlapping properties are examined. Coherent states are found to be similar to those found for a particle trapped in a P\"oschl-Teller potential of the trigonometric type. Some comparisons with Barut-Girardello and Klauder-Perelomov methods are noticed.Comment: 12 pages, clarifications and references added, misprints correcte

Raising and lowering operators, factorization and differential/difference operators of hypergeometric type

Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission

Mirror Inversion of Quantum States in Linear Registers

Transfer of data in linear quantum registers can be significantly simplified with pre-engineered but not dynamically controlled inter-qubit couplings. We show how to implement a mirror inversion of the state of the register in each excitation subspace with respect to the centre of the register. Our construction is especially appealing as it requires no dynamical control over individual inter-qubit interactions. If, however, individual control of the interactions is available then the mirror inversion operation can be performed on any substring of qubits in the register. In this case a sequence of mirror inversions can generate any permutation of a quantum state of the involved qubits.Comment: 4 page

Extensions of discrete classical orthogonal polynomials beyond the orthogonality

It is well known that the family of Hahn polynomials $\{h_n^{\alpha,\beta}(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $\Delta$-Sobolev orthogonality. We also present an analogous result for dual-Hahn, Krawtchouk, and Racah polynomials and give the limit relations between them for all n\in \XX N_0. Furthermore, in order to get this results for the Krawtchouk polynomials we will get a more general property of orthogonality for Meixner polynomials.Comment: 2 figures, 20 page

qq-Classical orthogonal polynomials: A general difference calculus approach

It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator. In this paper we present a study of classical orthogonal polynomials in a more general context by using the differential (or difference) calculus and Operator Theory. In such a way we obtain a unified representation of them. Furthermore, some well known results related to the Rodrigues operator are deduced. A more general characterization Theorem that the one given in [1] and [2] for the q-polynomials of the q-Askey and Hahn Tableaux, respectively, is established. Finally, the families of Askey-Wilson polynomials, q-Racah polynomials, Al-Salam & Carlitz I and II, and q-Meixner are considered. [1] R. Alvarez-Nodarse. On characterization of classical polynomials. J. Comput. Appl. Math., 196:320{337, 2006. [2] M. Alfaro and R. Alvarez-Nodarse. A characterization of the classical orthogonal discrete and q-polynomials. J. Comput. Appl. Math., 2006. In press.Comment: 18 page

Generally Deformed Oscillator, Isospectral Oscillator System and Hermitian Phase Operator

The generally deformed oscillator (GDO) and its multiphoton realization as well as the coherent and squeezed vacuum states are studied. We discuss, in particular, the GDO depending on a complex parameter q (therefore we call it q-GDO) together with the finite dimensional cyclic representations. As a realistic physical system of GDO the isospectral oscillator system is studied and it is found that its coherent and squeezed vacuum states are closely related to those of the oscillator. It is pointed out that starting from the q-GDO with q root of unity one can define the hermitian phase operators in quantum optics consistently and algebraically. The new creation and annihilation operators of the Pegg-Barnett type phase operator theory are defined by using the cyclic representations and these operators degenerate to those of the ordinary oscillator in the classical limit q->1.Comment: 21 pages, latex, no figure

Light Front Formalism for Composite Systems and Some of Its Applications in Particle and Relativistic Nuclear Physics

Light front formalism for composite systems is presented. Derivation of equations for bound state and scattering problems are given. Methods of constructing of elastic form factors and scattering amplitudes of composite particles are reviewed. Elastic form factors in the impulse approximation are calculated. Scattering amplitudes for relativistic bound states are constructed. Some model cases for transition amplitudes are considered. Deep inelastic form factors (structure functions) are expressed through light front wave functions. It is shown that taking into account of transverse motion of partons leads to the violation of Bjorken scaling and structure functions become square of transverse momentum dependent. Possible explanation of the EMC-effect is given. Problem of light front relativization of wave functions of lightest nuclei is considered. Scaling properties of deuteron, ${}^3He$ and ${}^4He$ light front wave functions are checked in a rather wide energy range.Comment: Review paper, Submitted to Phys. Rep., 89 pages, 23 figure

Hydrogeology of south-east part of caspian coastal depression in connection with its oil- and gas-bearing capacity

Purpose of the work: development of the hydrogeological bases of the oil and gas accumulation and prediction of the industrial oil- and gas-bearing capacity in the highly prospective south-east part of the Caspian coastal depression. The investigation reveals zones, peculiarities of spatial differentiation, interconditionality and interconnection of the hydrogeological fields. It determines the presence and domination of the transfer-injection hydrodynamic system in the sedimentary section of the region. Hydrogeological oil and gas accumulation areas of the region are developed. The investigation provides a scientifically grounded prognosis of the existence and spatial location of the industrical oil- and gas-bearing capacities in the region which can contribute to the optimization and increase of the effectiveness of the geological and exploration workAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio