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Exact polynomial eigensolutions of the Schrodinger equation for the pseudoharmonic potential
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Date
2007-03-31
Author
Ikhdair, Sameer
Sever, Ramazan
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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.
Subject Keywords
Pseudoharmonic potential
,
Anharmonic oscillator potential
,
Schrodinger equation
,
Diatomic molecules
,
Eigenvalues and eigenfunction
,
Bound states
URI
https://hdl.handle.net/11511/62476
Journal
JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM
DOI
https://doi.org/10.1016/j.theochem.2006.11.019
Collections
Department of Physics, Article
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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.
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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 eigenso...
Analytical solutions of Schrodinger equation for the diatomic molecular potentials with any angular momentum
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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.
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S. Ikhdair and R. Sever, “Exact polynomial eigensolutions of the Schrodinger equation for the pseudoharmonic potential,”
JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM
, pp. 155–158, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62476.