302 research outputs found
Systematic Search of Exactly Solvable Non-Central Potentials
Recently developed supersymmetric perturbation theory has been successfully
employed to make a complete mathematical analysis the reason behind exact
solvability of some non-central potentials. This investigation clarifies once
more the effectiveness of the present formalism.Comment: 7 pages, no figure
A simple model potential for hollow nanospheres
A new model potential is introduced to describe the hollow nanospheres such
as fullerene and molecular structures and to obtain their electronic
properties. A closed analytical solution of the corresponding treatment is
given within the framework of supersymmetric perturbation theory.Comment: 7 pages, 3 figure
Bound State Solutions of Klein-Gordon Equation with the Kratzer Potential
The relativistic problem of spinless particle subject to a Kratzer potential
is analyzed. Bound state solutions for the s-wave are found by separating the
Klein-Gordon equation in two parts, unlike the similar works in the literature,
which provides one to see explicitly the relativistic contributions, if any, to
the solution in the non-relativistic limit.Comment: 6 page
Explicit Solutions for N-Dimensional Schrodinger Equations with Position-Dependent Mass
With the consideration of spherical symmetry for the potential and mass
function, one-dimensional solutions of non-relativistic Schrodinger equations
with spatially varying effective mass are successfully extended to arbitrary
dimensions within the frame of recently developed elegant non-perturbative
technique, where the BenDaniel-Duke effective Hamiltonian in one-dimension is
assumed like the unperturbed piece, leading to well-known solutions, whereas
the modification term due to possible use of other effective Hamiltonians in
one-dimension and, together with, the corrections coming from the treatments in
higher dimensions are considered as an additional term like the perturbation.
Application of the model and its generalization for the completeness are
discussed.Comment: 8 pages, no figure
A search on Dirac equation
The solutions, in terms of orthogonal polynomials, of Dirac equation with
analytically solvable potentials are investigated within a novel formalism by
transforming the relativistic equation into a Schrodinger like one. Earlier
results are discussed in a unified framework and certain solutions of a large
class of potentials are given.Comment: 9 page
A search on the Nikiforov-Uvarov formalism
An alternative treatment is proposed for the calculations carried out within
the frame of Nikiforov-Uvarov method, which removes a drawback in the original
theory and by pass some difficulties in solving the Schrodinger equation. The
present procedure is illustrated with the example of orthogonal polynomials.
The relativistic extension of the formalism is discussed.Comment: 10 page
Two Electrons in a Quantum Dot: A Unified Approach
Low-lying energy levels of two interacting electrons confined in a
two-dimensional parabolic quantum dot in the presence of an external magnetic
field have been revised within the frame of a novel model. The present
formalism, which gives closed algebraic solutions for the specific values of
magnetic field and spatial confinement length, enables us to see explicitly
individual effects of the electron correlation.Comment: 14 page
A perturbative treatment for the energy levels of neutral atoms
Energy levels of neutral atoms have been re-examined by applying an
alternative perturbative scheme in solving the Schrodinger equation for the
Yukawa potential model with a modified screening parameter. The predicted shell
binding energies are found to be quite accurate over the entire range of the
atomic number up to 84 and compare very well with those obtained within the
framework of hyper-virial-Pade scheme and the method of shifted large-N
expansion. It is observed that the new perturbative method may also be applied
to the other areas of atomic physics.Comment: 18 page
Mapping of non-central potentials under point canonical transformations
Motivated by the observation that all known exactly solvable shape invariant
central potentials are inter-related via point canonical transformations, we
develop an algebraic framework to show that a similar mapping procedure is also
exist between a class of non-central potentials. As an illustrative example, we
discuss the inter-relation between the generalized Coulomb and oscillator
systems.Comment: 11 pages article in LaTEX (uses standard article.sty). Please check
http://www1.gantep.edu.tr/~gonul for other studies of Nuclear Physics Group
at University of Gaziante
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