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Keywords:

  • Darboux transformation;
  • two-level system;
  • quantum dot

Abstract

We develop the Darboux procedure for the case of the two-level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two-level system, transforming only one real potential into another real potential. We apply the obtained Darboux transformation to known exact solutions of the two-level system. Thus, we find three classes of new solutions for the two-level system and the corresponding new potentials that allow such solutions.