On solutions of the Schrodinger equation for some molecular potentials: wave function ansatz

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2008-09-01

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IKHDAİR, SAMEER
Sever, Ramazan

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Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrodinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, delta and nu are also given, where eta depends on a linear combination of the angular momentum quantum number l and the spatial dimensions D and delta is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.

Subject Keywords

optical character recognition, Diatomic molecules, Schrodinger equation, Anharmonic oscillator potential, Mie-type potential, Kratzer's potential, Pseudoharmonic potential, Bound states

URI

https://hdl.handle.net/11511/62579

Journal

CENTRAL EUROPEAN JOURNAL OF PHYSICS

DOI

https://doi.org/10.2478/s11534-008-0060-y

Collections

Department of Physics, Article

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Approximate analytical solutions of a two-term diatomic molecular potential with centrifugal barrier Arda, Altug; Sever, Ramazan (2012-08-01) Approximate analytical bound state solutions of the radial Schrodinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where q >= 1 and q = 0. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulthen potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.
Analytical solutions of Schrodinger equation for the diatomic molecular potentials with any angular momentum Akçay, Hüseyin; Sever, Ramazan (2012-08-01) Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also considered. Algebraic method is used in the calculations.
Polynomial solutions of the Mie-type potential in the D-dimensional Schrodinger equation IKHDAİR, SAMEER; Sever, Ramazan (2008-04-30) The polynomial solution of the D-dimensional Schrodinger equation for a special case of Mie potential is obtained with an arbitrary l not equal 0 states. The exact bound state energies and their corresponding wave functions are calculated. The bound state (real) and positive (imaginary) cases are also investigated. In addition, we have simply obtained the results from the solution of the Coulomb potential by an appropriate transformation.
Exact solutions of the radial Schrodinger equation for some physical potentials IKHDAİR, SAMEER; Sever, Ramazan (2007-12-01) By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained. (C) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.

Citation Formats

S. IKHDAİR and R. Sever, “On solutions of the Schrodinger equation for some molecular potentials: wave function ansatz,” CENTRAL EUROPEAN JOURNAL OF PHYSICS, pp. 697–703, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62579.