Abstract
The second-order Darboux transform for a growing potential of a Schrödinger equation is discussed in detail. Restrictions on the transforming functions whose eigenvalues are greater than the energy of the ground state if the potential of the transformed Schrödinger equation is regular has been established. It has been shown that, along with the well-known elimination of two levels of the discrete spectrum, other opportunities can also be realized: (a) the transformed spectrum remains identical to the original one; (b) one level is eliminated from the spectrum; (c) one additional level is generated, and (d) two additional levels are generated.
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Bagrov, V.G., Samsonov, B.F. On Irreducible Second-Order Darboux Transformations. Russian Physics Journal 45, 27–33 (2002). https://doi.org/10.1023/A:1016037502390
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DOI: https://doi.org/10.1023/A:1016037502390