Darboux Transformation in the Tangent-Squared Potential and Supersymmetry

Abstract

In this paper, we consider one-dimensional Schrödinger equation for the trigonometric tangent-squared potential. Here, we construct the first-order Darboux transformation and the real valued condition of transformed potential for trigonometric tangent-squared potential equation. Also we obtain the transformed of potential and wave function. Finally, we discuss the correspondence between Darboux transformation and supersymmetry. In order to have supersymmetry and commutative and anti-commutative algebra, we obtain some condition for the corresponding equation.