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A supersymmetric technique for the solution of the effective mass Schrödinger equation is proposed. Exact solutions of the Schrödinger equation corresponding to a number of potentials are obtained. The potentials are fully isospectral with the original potentials. The conditions for the shape invariance of the potentials are discussed.

A supersymmetric technique for the bound-state solutions of the s-wave Klein-Gordon equation with equal scalar and vector standard Eckart type potential is proposed. Its exact solutions are obtained. Possible generalization of our approach is outlined.

We present a method to solve the problem of Rashba spinorbit coupling in semiconductor quantum dots, within the context of quasi-exactly solvable spectral problems. We show that the problem possesses a hidden osp(2, 2) superalgebra. We constructed a general matrix whose determinant provide exact eigenvalues. Analogous mathematical structures between the Rashba and some of the other spin-boson physical systems are notified.PACS numbers:

The bound state solution of the (1+1)-dimensional Klein–Gordon (KG) equation for the generalized Hulthén potential has been studied in the framework of the asymptotic iteration method (AIM). The energy values and the corresponding eigenfunctions are obtained for mixed forms of the Hulthén vector potential and scalar potential.