Darboux Transformations for the Generalized SchrЁodinger Equation

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Abstract


The Darboux transformations of the n-th order is elaborated for a generalized Schr̈odinger equation with a position-dependent effective mass and with a linearly energy-dependent potential. The Darboux transformations are given also in an integral form. A correspondence between the differential Darboux transformations and the integral ones has been established. The second-order Darboux transformations are analyzed both at different energies and at the same transformation energy. The method is illustrated by several examples of constructing quantum potential wells with a given spectrum.

About the authors

A A Suzko

Joint Institute for Nuclear Research

Email: suzko@jinr.ru
Лаборатория информационных технологийОбъединённый институт энергетических и ядерных исследований НАН Р. Беларусьул. акад. А.К. Красина, 99, Минск, 220109, Республика Беларусь; Объединённый институт ядерных исследований; Joint Institute for Nuclear Research

E P Velicheva

Joint Institute for Nuclear Research

Email: velicheva@jinr.ru
Лаборатория ядерных проблем; Объединённый институт ядерных исследований; Joint Institute for Nuclear Research

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Copyright (c) 2011 Сузько А.А., Величева Е.П.

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