Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Effective polar potential in the central force Schrodinger equation
Download
index.pdf
Date
2010-01-01
Author
Shikakhwa, M. S.
Mustafa, M.
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
143
views
0
downloads
Cite This
The angular part of the Schrodinger equation for a central potential is brought to the one-dimensional 'Schrodinger form' where one has a kinetic energy plus potential energy terms. The resulting polar potential is seen to be a family of potentials characterized by the square of the magnetic quantum number m. It is demonstrated that this potential can be viewed as a confining potential that attempts to confine the particle to the xy-plane, with a strength that increases with increasing m. Linking the solutions of the equation to the conventional solutions of the angular equation, i.e. the associated Legendre functions, we show that the variation in the spatial distribution of the latter for different values of the orbital angular quantum number l can be viewed as being a result of 'squeezing' with different strengths by the introduced 'polar potential'.
Subject Keywords
General Physics and Astronomy
URI
https://hdl.handle.net/11511/65364
Journal
EUROPEAN JOURNAL OF PHYSICS
DOI
https://doi.org/10.1088/0143-0807/31/1/014
Collections
Natural Sciences and Mathematics, Article
Suggestions
OpenMETU
Core
Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields
Eshghi, M.; Sever, Ramazan; Ikhdair, S. M. (IOP Publishing, 2018-02-01)
We need to solve a suitable exponential form of the position-dependent mass (PDM) Schrodinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov-Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.
Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials
IKHDAİR, SAMEER; Sever, Ramazan (Wiley, 2009-10-01)
The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P-n((mu,nu)) (x), where mu > -1, nu > -1 and x is an element of[-1, +1]. The s-waves analytic solution is obtained. Th...
Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit
Aydogdu, Oktay; Sever, Ramazan (Elsevier BV, 2010-02-01)
We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term K. We also investigate the energ...
Effective Mass Schrodinger Equation via Point Canonical Transformation
Arda, Altug; Sever, Ramazan (IOP Publishing, 2010-07-01)
Exact solutions of the effective radial Schrodinger equation are obtained for some inverse potentials by using the point canonical transformation. The energy eigenvalues and the corresponding wave functions are calculated by using a set of mass distributions.
Approximate solution to the time-dependent Kratzer plus screened Coulomb potential in the Feinberg-Horodecki equation
Farout, Mahmoud; Sever, Ramazan; Ikhdair, Sameer M. (IOP Publishing, 2020-06-01)
We obtain the quantized momentum eigenvalues P-n together with space-like coherent eigenstates for the space-like counterpart of the Schrodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. S. Shikakhwa and M. Mustafa, “Effective polar potential in the central force Schrodinger equation,”
EUROPEAN JOURNAL OF PHYSICS
, pp. 151–156, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65364.