This article is cited in 20 scientific papers (total in 20 papers)
Darboux transformation, factorization, supersymmetry in one-dimensional quantum mechanics
V. G. Bagrova, B. F. Samsonovb
a Tomsk State University
b Institute of High Current Electronics, Siberian Branch of the Russian Academy of Sciences
We introduce an $N$-order Darboux transformation operator as a particular case of general transformation operators. It is shown that this operator can always be represented as a product of $N$ first-order Darboux transformation operators. The relationship between this transformation and the factorization method is investigated. Supercharge operators are introduced. They are differential operators of order $N$. It is shown that these operators and super-Hamiltonian form a superalgebra of order $N$. For $N=2$, we have a quadratic superalgebra analogous to the Sklyanin quadratic algebras. The relationship between the transformation introduced and the inverse scattering problem in quantum mechanics is established. An elementary $N$-parametric potential that has exactly $N$ predetermined discrete spectrum levels is constructed. The paper concludes with some examples of new exactly soluble potentials.
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Theoretical and Mathematical Physics, 1995, 104:2, 1051–1060
V. G. Bagrov, B. F. Samsonov, “Darboux transformation, factorization, supersymmetry in one-dimensional quantum mechanics”, TMF, 104:2 (1995), 356–367; Theoret. and Math. Phys., 104:2 (1995), 1051–1060
Citation in format AMSBIB
\by V.~G.~Bagrov, B.~F.~Samsonov
\paper Darboux transformation, factorization, supersymmetry in one-dimensional quantum mechanics
\jour Theoret. and Math. Phys.
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