Darboux transformation for two-level systems
V.G. Bagrov, M.C. Baldiotti, D.M. Gitman, V.V. Shamshutdinova
TL;DR
This paper develops a Darboux transformation method tailored for two-level quantum systems, enabling the generation of new solutions and potentials while preserving the system's structure.
Contribution
It introduces a Darboux intertwining operator that maintains the two-level system's structure and constructs new solutions and potentials.
Findings
Constructed a Darboux operator that preserves the two-level system structure.
Generated three new classes of solutions and potentials.
Applied the transformation to known solutions to find new ones.
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.
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