Explicit formulas for generalized harmonic perturbations of the infinite quantum well with an application to Mathieu equations

Journal Article · Mon Oct 15 00:00:00 EDT 2012 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4750222· OSTI ID:22093750

Garcia-Ravelo, J.; Trujillo, A. L. ^[1]; Schulze-Halberg, A. ^[2]

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1. Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Unidad Profesional Adolfo Lopez Mateos, Zacatenco, 07738 Mexico D.F. (Mexico)
2. Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schroedinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.

• OSTI ID: 22093750
• Journal Information: Journal of Mathematical Physics, Vol. 53, Issue 10; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRECTIONS
DISTURBANCES
MATHEMATICAL SOLUTIONS
MATHIEU EQUATION
MATRIX ELEMENTS
NONLINEAR PROBLEMS
PERIODICITY
PERTURBATION THEORY
QUANTUM WELLS
SCHROEDINGER EQUATION