The cross-additivity-two parameters shape invariance of superpotential Bcscαx-Acotαx based on SUSYQM.

• This paper solves the Schrödinger equation with the partner potentials generated by the superpotential (B Csc αx - A Cot αx). • The additivity shape invariance with two parameters is discussed in detail. • The shape invariance of the partner potentials of the two parameters shows cross-additivity characteristics which is entirely different from the general additivity characteristics. • Through the potential algebra method, we discuss again the shape invariance of the partner potentials generated by the two parameters with cross-additivity characteristics. • We obtain the energy eigenvalue and the recursion relation of the wave function with even energy level number. Supersymmetric quantum mechanics is an effective method to solve the exact solution of the Schrödinger equation. This paper studies the solution of the Schrödinger equation with the partner potentials generated by the superpotential (B csc α x - A cot α x) with two parameters (A and B). Firstly, the shape invariance of the partner potentials generated by the superpotential is obtained. The parametric additivity of shape invariance satisfies a special additivity characteristic: the two-parameter cross-additivity (A → B + α 2 , B → A + α 2) , which is completely different from the general additivity characteristic (A → A + α 2 , B → B + α 2). Secondly, we discuss the case that belongs to two-parameter cross additive shape invariance in detail, and find that this two-parameter cross-additivity resulted in partial states missing. The existing energy spectrum and eigenfunctions of the Schrödinger equation with this new parametric transformation are worked out. Thirdly, we discuss the Shape invariance of the partner potentials generated again by the two parameters with cross additive characteristics through the potential algebra method. Lastly, the conclusions and discussions are made. [ABSTRACT FROM AUTHOR]