Darboux transformation coupled quantum adiabatic switching: A viable way for simultaneous generation of eigen spectra

This article endeavours to provide a methodological development for generation of eigen- spectrum of given quantum mechanical potential, employing a combination of Darboux transformation and quantum adiabatic switching theorem, bypassing direct solution of Schrödinger equation. Here, Darboux potential is derived directly from Riccati equation, a first-order non-linear differential equation, and from that Darboux potential, the ground eigen-state is generated. Considering that ground eigen-state as initial wave-function in the adiabatic switching process, ground eigen-state of the partner Hamiltonian is obtained. Subsequently, applying proper Darboux charge operator, first excited eigen-state of the initial Hamiltonian is procured. Repetition of the process of switching and execution of Darboux operator leads to simultaneous generation of eigen-spectra for both Darboux partners. Application of the proposed method in model potentials yields results, qualitatively consistent with known observations. Moreover, calculation of quantum information entropy during switching leads to estimation of change in thermodynamic entropy for corresponding physical processes.