2,873 research outputs found
Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method
For non-zero values, we present an analytical solution of the radial
Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris
approximation within the framework of the Asymptotic Iteration Method. The
bound state energy eigenvalues and corresponding wave functions are obtained
for a number of diatomic molecules and the results are compared with the
findings of the super-symmetry, the hypervirial perturbation, the
Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N
expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of
Physics A: Mathematical and Genera
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
Overlap integral for quantum skyrmions
We made use a simplified form for the quantum skyrmion wave function based on
the spin coherent states to obtain the analytical expression for appropriate
overlap integral.Comment: 5 pages, no figure
Crystal structure of mixed fluorites Ca(1-x)Sr(x)F(2) and Sr(1-x)Ba(x)F(2) and luminescence of Eu(2+) in the crystals
Within the framework of the virtual crystal method implemented in the shell
model and pair potential approximation the crystal structure of mixed fluorites
Ca(1-x)Sr(x)F(2) and Sr(1-x)Ba(x)F(2) has been calculated. The impurity center
Eu(2+) and the distance Eu(2+)-F in this crystals have been also calculated.
The low level position of excited 4f65d configuration of the Eu(2+) ion has
been expressed using phenomenological dependence on distance E(2+)-F. The
dependences of Stokes shift and Huang-Rhys factor on concentration x have been
received for yellow luminescence in Sr(1-x)Ba(x)F(2):Eu(2+). The value x, for
which the eg -level of Eu(2+) ion will be in conduction band in
Sr(1-x)Ba(x)F(2):Eu(2+) has been calculated.Comment: 8 pages, 3 figures. The manuscript is sent to journal 'Physics of the
solid state'. The results will be submitted on inernational conference
SCINTMAT'2002 in oral session (june,20-22,2002,Ekaterinburg,Russia).
Corresponding author e-mail: [email protected]
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
Landau (\Gamma,\chi)-automorphic functions on \mathbb{C}^n of magnitude \nu
We investigate the spectral theory of the invariant Landau Hamiltonian
\La^\nu acting on the space of
-automotphic functions on \C^n, for given real number ,
lattice of \C^n and a map such that the
triplet satisfies a Riemann-Dirac quantization type
condition. More precisely, we show that the eigenspace
{\mathcal{E}}^\nu_{\Gamma,\chi}(\lambda)=\set{f\in
{\mathcal{F}}^\nu_{\Gamma,\chi}; \La^\nu f = \nu(2\lambda+n) f};
\lambda\in\C, is non trivial if and only if . In such
case, is a finite dimensional vector space
whose the dimension is given explicitly. We show also that the eigenspace
associated to the lowest Landau level of
\La^\nu is isomorphic to the space, {\mathcal{O}}^\nu_{\Gamma,\chi}(\C^n),
of holomorphic functions on \C^n satisfying g(z+\gamma) = \chi(\gamma)
e^{\frac \nu 2 |\gamma|^2+\nu\scal{z,\gamma}}g(z), \eqno{(*)} that we can
realize also as the null space of the differential operator
acting on
functions on \C^n satisfying .Comment: 20 pages. Minor corrections. Scheduled to appear in issue 8 (2008) of
"Journal of Mathematical Physics
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