Green's functions and trace formulas for generalized Sturm-Liouville problems related by Darboux transformations

Journal Article · Sat May 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3407605· OSTI ID:21335966

Schulze-Halberg, Axel ^[1]

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1. Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

We study Green's functions of the generalized Sturm-Liouville problems that are related to each other by Darboux -equivalently, supersymmetrical - transformations. We establish an explicit relation between the corresponding Green's functions and derive a simple formula for their trace. The class of equations considered here includes the conventional Schroedinger equation and generalizations, such as for position-dependent mass and with linearly energy-dependent potential, as well as the stationary Fokker-Planck equation.

• OSTI ID: 21335966
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 5; Other Information: DOI: 10.1063/1.3407605; (c) 2010 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
ENERGY DEPENDENCE
FOKKER-PLANCK EQUATION
GREEN FUNCTION
MASS
POTENTIALS
SCHROEDINGER EQUATION
STURM-LIOUVILLE EQUATION
TRANSFORMATIONS