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Analytical solutions of Schrodinger equation for the diatomic molecular potentials with any angular momentum
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Date
2012-08-01
Author
Akçay, Hüseyin
Sever, Ramazan
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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.
Subject Keywords
Diatomic molecular potential
,
Exact solutions
,
Bound-states
,
Energy eigenvalues
,
Wave functions
,
Schrodinger equation
,
Algebraic method
URI
https://hdl.handle.net/11511/62540
Journal
JOURNAL OF MATHEMATICAL CHEMISTRY
DOI
https://doi.org/10.1007/s10910-012-0013-y
Collections
Department of Physics, Article
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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.
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.
Exact solution of Schrodinger equation for Pseudoharmonic potential
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Exact solution of Schrodinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The energy eigenvalues are calculated numerically for some values of l and n with n <= 5 for some diatomic molecules.
Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum
Akçay, Hüseyin; Sever, Ramazan (2013-11-01)
Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Poschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.
On solutions of the Schrodinger equation for some molecular potentials: wave function ansatz
IKHDAİR, SAMEER; Sever, Ramazan (2008-09-01)
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 eigenso...
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H. Akçay and R. Sever, “Analytical solutions of Schrodinger equation for the diatomic molecular potentials with any angular momentum,”
JOURNAL OF MATHEMATICAL CHEMISTRY
, pp. 1973–1987, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62540.