Effective mass Schrodinger equation for exactly solvable class of one-dimensional potentials

Aktas, Metin
Sever, Ramazan
We deal with the exact solutions of Schrodinger equation characterized by position-dependent effective mass via point canonical transformations. The Morse, Poschl-Teller, and Hulthen type potentials are considered, respectively. With the choice of position-dependent mass forms, exactly solvable target potentials are constructed. Their energy of the bound states and corresponding wavefunctions are determined exactly.


Exact solutions of the schrodinger equation with position-dependent effective mass via general point canonical transformation
Tezcan, Cevdet; Sever, Ramazan (2007-10-01)
Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.
Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances
AYDOĞDU, OKTAY; Arda, Altug; Sever, Ramazan (2012-04-01)
Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are calculated by using behavior of the wave functions at infinity. The same analysis is done for the constant mass case. It is also pointed out that our results are in agreement with those obtained in literature. Meanwhile, an analytic expression is obtained for the transmissi...
Exact solution of effective mass Schrodinger equation for the Hulthen potential
Sever, Ramazan; TEZCAN, CEVDET; Yesiltas, Oezlem; Bucurgat, Mahmut (2008-09-01)
A general form of the effective mass Schrodinger equation is solved exactly for Hulthen 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.
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.
Exact polynomial eigensolutions of the Schrodinger equation for the pseudoharmonic potential
Ikhdair, Sameer; Sever, Ramazan (2007-03-31)
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum l. The exact bound-state energy eigenvalues and the corresponding eigenfunctions are analytically calculated. The energy states for several diatomic molecular systems are calculated numerically for various principal and angular quantum numbers. By a proper transformation, this problem is also solved very simply by using the known eigensolutions of anharmonic oscillator potential.
Citation Formats
M. Aktas and R. Sever, “Effective mass Schrodinger equation for exactly solvable class of one-dimensional potentials,” JOURNAL OF MATHEMATICAL CHEMISTRY, pp. 92–100, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62674.