Abstract
Darboux transformations of a regular Sturm-Liouville problem are considered. A relationship between the Green’s functions of the initial and transformed problems is found. Second-order reducible and irreducible Darboux transformations are analyzed. It is demonstrated that a new second-order irreducible supersymmetry can exist in the regular case for which the spectrum of the intermediate Hamiltonian differs radically from the spectrum of the initial Hamiltonian. The results obtained are illustrated by the example of a particle in a box.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 20–26, October, 2005.
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Samsonov, B.F., Pupasov, A.M. Darboux transformation of the Green’s function of a regular Sturm-Liouville problem. Russ Phys J 48, 1020–1028 (2005). https://doi.org/10.1007/s11182-006-0021-0
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DOI: https://doi.org/10.1007/s11182-006-0021-0