Sextic and decatic anharmonic oscillator potentials including odd power terms: Polynomial solutions

We study the sextic and decatic potentials energy including the odd power terms, and explore possible polynomial solutions for Schrödinger equation. Moreover, we proved that generals sextic and decatic potentials are exactly solvable under certain conditions on the potential’s parameters; these cond...

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Bibliographic Details
Main Authors: Maiz, F., Alqahtani, Moteb M., Ghnaim, I.
Format: Conference Proceeding
Language:English
Subjects:
Anharmonicity
Eigenvectors
Energy levels
Numerical methods
Parameters
Polynomials
Schrodinger equation
Online Access:Get full text
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Summary:We study the sextic and decatic potentials energy including the odd power terms, and explore possible polynomial solutions for Schrödinger equation. Moreover, we proved that generals sextic and decatic potentials are exactly solvable under certain conditions on the potential’s parameters; these conditions connect the potential’s parameters to each other and to wave function’s zeros. We compare achieved results with those evaluated by numerical methods. Finally, we derive general expressions of the energy levels and evaluate the first eigenstates for both potentials.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5042401