42 research outputs found
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
is orthogonal with respect to a certain
weight function up to . In this paper we present a factorization for Hahn
polynomials for a degree higher than and we prove that these polynomials
can be characterized by a -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
-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, and
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