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Exact solution of Schrodinger equation for Pseudoharmonic potential
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Date
2008-02-01
Author
Sever, Ramazan
TEZCAN, CEVDET
Aktas, Metin
Yesiltas, Oezlem
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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.
Subject Keywords
Schrodinger equation
,
Nikiforov-Uvarov method
,
Diatomic molecules
,
Pseudoharmonic potential
URI
https://hdl.handle.net/11511/62900
Journal
JOURNAL OF MATHEMATICAL CHEMISTRY
DOI
https://doi.org/10.1007/s10910-007-9233-y
Collections
Department of Physics, Article
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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.
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Exact solution of the Schrodinger equation with deformed ring-shaped potential is obtained in the parabolic and spherical coordinates. The Nikiforov-Uvarov method is used in the solution. Eigenfunctions and corresponding energy eigenvalues are calculated analytically. The agreement of our results is good.
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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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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.
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R. Sever, C. TEZCAN, M. Aktas, and O. Yesiltas, “Exact solution of Schrodinger equation for Pseudoharmonic potential,”
JOURNAL OF MATHEMATICAL CHEMISTRY
, pp. 845–851, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62900.