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

Journal Article · · Journal of Mathematical Physics
DOI:https://doi.org/10.1063/1.3407605· OSTI ID:21335966
 [1]
  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, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
Country of Publication:
United States
Language:
English

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