297 research outputs found
A high order -difference equation for -Hahn multiple orthogonal polynomials
A high order linear -difference equation with polynomial coefficients
having -Hahn multiple orthogonal polynomials as eigenfunctions is given. The
order of the equation is related to the number of orthogonality conditions that
these polynomials satisfy. Some limiting situations when are studied.
Indeed, the difference equation for Hahn multiple orthogonal polynomials given
in \cite{Lee} is corrected and obtained as a limiting case
Shape invariant hypergeometric type operators with application to quantum mechanics
A hypergeometric type equation satisfying certain conditions defines either a
finite or an infinite system of orthogonal polynomials. The associated special
functions are eigenfunctions of some shape invariant operators. These operators
can be analysed together and the mathematical formalism we use can be extended
in order to define other shape invariant operators. All the considered shape
invariant operators are directly related to Schrodinger type equations.Comment: More applications available at http://fpcm5.fizica.unibuc.ro/~ncotfa
-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
The Schrodinger equation with Hulthen potential plus ring-shaped potential
We present the solutions of the Schrdinger equation with the
Hulthn potential plus ring-shape potential for states
within the framework of an exponential approximation of the centrifugal
potential.Solutions to the corresponding angular and radial equations are
obtained in terms of special functions using the conventional Nikiforov-Uvarov
method. The normalization constant for the Hulthn potential is also
computed.Comment: Typed with LateX,12 Pages, Typos correcte
Gazeau-Klauder type coherent states for hypergeometric type operators
The hypergeometric type operators are shape invariant, and a factorization
into a product of first order differential operators can be explicitly
described in the general case. Some additional shape invariant operators
depending on several parameters are defined in a natural way by starting from
this general factorization. The mathematical properties of the eigenfunctions
and eigenvalues of the operators thus obtained depend on the values of the
involved parameters. We study the parameter dependence of orthogonality, square
integrability and of the monotony of eigenvalue sequence. The obtained results
allow us to define certain systems of Gazeau-Klauder coherent states and to
describe some of their properties. Our systematic study recovers a number of
well-known results in a natural unified way and also leads to new findings.Comment: An error occurring in Theorem 12 and Theorem 13 has been correcte
Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields
We construct an explicit solution of the Cauchy initial value problem for the
time-dependent Schroedinger equation for a charged particle with a spin moving
in a uniform magnetic field and a perpendicular electric field varying with
time. The corresponding Green function (propagator) is given in terms of
elementary functions and certain integrals of the fields with a characteristic
function, which should be found as an analytic or numerical solution of the
equation of motion for the classical oscillator with a time-dependent
frequency. We discuss a particular solution of a related nonlinear Schroedinger
equation and some special and limiting cases are outlined.Comment: 17 pages, no figure
A new approach to the exact solutions of the effective mass Schrodinger equation
Effective mass Schrodinger equation is solved exactly for a given potential.
Nikiforov-Uvarov method is used to obtain energy eigenvalues and the
corresponding wave functions. A free parameter is used in the transformation of
the wave function. The effective mass Schrodinger equation is also solved for
the Morse potential transforming to the constant mass Schr\"{o}dinger equation
for a potential. One can also get solution of the effective mass Schrodinger
equation starting from the constant mass Schrodinger equation.Comment: 14 page
Approximate Solution of the effective mass Klein-Gordon Equation for the Hulthen Potential with any Angular Momentum
The radial part of the effective mass Klein-Gordon equation for the Hulthen
potential is solved by making an approximation to the centrifugal potential.
The Nikiforov-Uvarov method is used in the calculations. Energy spectra and the
corresponding eigenfunctions are computed. Results are also given for the case
of constant mass.Comment: 12 page
Exact solution of Schrodinger equation for Pseudoharmonic potential
Exact solution of Schrodinger equation for the pseudoharmonic potential is
obtained for an arbitrary angular momentum. The energy eigenvalues and
corresponding eigenfunctions are calculated by Nikiforov-Uvarov method.
Wavefunctions are expressed in terms of Jacobi polynomials. The energy
eigenvalues are calculated numerically for some values of l and n with n<5 for
some diatomic molecules.Comment: 10 page
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