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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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
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Alqahtani, Moteb M.
Ghnaim, I.
description 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.
doi_str_mv 10.1063/1.5042401
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source American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list)
subjects Anharmonicity
Eigenvectors
Energy levels
Numerical methods
Parameters
Polynomials
Schrodinger equation
title Sextic and decatic anharmonic oscillator potentials including odd power terms: Polynomial solutions
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