2,318 research outputs found
Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices
We give a uniform interpretation of the classical continuous Chebyshev's and
Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie
algebra gl(N), where N is any complex number. One can similarly interpret
Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials
corresponding to Lie superlagebras.
We also describe the real forms of gl(N), quasi-finite modules over gl(N),
and conditions for unitarity of the quasi-finite modules. Analogs of tensors
over gl(N) are also introduced.Comment: 25 pages, LaTe
Mathematical Structure of Relativistic Coulomb Integrals
We show that the diagonal matrix elements where
are the standard Dirac matrix operators
and the angular brackets denote the quantum-mechanical average for the
relativistic Coulomb problem, may be considered as difference analogs of the
radial wave functions. Such structure provides an independent way of obtaining
closed forms of these matrix elements by elementary methods of the theory of
difference equations without explicit evaluation of the integrals. Three-term
recurrence relations for each of these expectation values are derived as a
by-product. Transformation formulas for the corresponding generalized
hypergeometric series are discussed.Comment: 13 pages, no figure
Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential
The bound state energy eigenvalues and the corresponding eigenfunctions of
the generalized Woods Saxon potential are obtained in terms of the Jacobi
polynomials. Nikiforov Uvarov method is used in the calculations. It is shown
that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review
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
Physical applications of second-order linear differential equations that admit polynomial solutions
Conditions are given for the second-order linear differential equation P3 y"
+ P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of
degree n. Several application of these results to Schroedinger's equation are
discussed. Conditions under which the confluent, biconfluent, and the general
Heun equation yield polynomial solutions are explicitly given. Some new classes
of exactly solvable differential equation are also discussed. The results of
this work are expressed in such way as to allow direct use, without preliminary
analysis.Comment: 13 pages, no figure
h analogue of Newton's binomial formula
In this letter, the --analogue of Newton's binomial formula is obtained in
the --deformed quantum plane which does not have any --analogue. For
, this is just the usual one as it should be. Furthermore, the binomial
coefficients reduce to for . \\ Some properties of the
--binomial coefficients are also given. \\ Finally, I hope that such results
will contribute to an introduction of the --analogue of the well--known
functions, --special functions and --deformed analysis.Comment: 6 pages, latex Jounal-ref: J. Phys. A: Math. Gen. 31 (1998) L75
Field momentum and gyroscopic dynamics of classical systems with topological defects
The standard relation between the field momentum and the force is generalized
for the system with a field singularity: in addition to the regular force,
there appear the singular one. This approach is applied to the description of
the gyroscopic dynamics of the classical field with topological defects. The
collective variable Lagrangian description is considered for gyroscopical
systems with account of singularities. Using this method we describe the
dynamics of two-dimensional magnetic solitons. We establish a relation between
the gyroscopic force and the singular one. An effective Lagrangian description
is discussed for the magnetic soliton dynamics.Comment: LaTeX, 19 page
Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential
The energy eigenvalues and the corresponding eigenfunctions of the
one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential
are analytically obtained within the position-dependent mass formalism. The
parametric generalization of the Nikiforov-Uvarov method is used in the
calculations by choosing a mass distribution.Comment: 10 page
Effective Mass Dirac-Morse Problem with any kappa-value
The Dirac-Morse problem are investigated within the framework of an
approximation to the term proportional to in the view of the
position-dependent mass formalism. The energy eigenvalues and corresponding
wave functions are obtained by using the parametric generalization of the
Nikiforov-Uvarov method for any -value. It is also studied the
approximate energy eigenvalues, and corresponding wave functions in the case of
the constant-mass for pseudospin, and spin cases, respectively.Comment: 12 page
Relativistic Kramers-Pasternack Recurrence Relations
Recently we have evaluated the matrix elements ,O={1,\beta, i\mathbf{\alpha n}\beta} _{3}F_{2}(1) $ for all suitable powers and established two sets of
Pasternack-type matrix identities for these integrals. The corresponding
Kramers--Pasternack three-term vector recurrence relations are derived here.Comment: 12 pages, no figures Will appear as it is in Journal of Physics B:
Atomic, Molecular and Optical Physics, Special Issue on Hight Presicion
Atomic Physic
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