Exact Solutions of the Position-dependent Mass Schrödinger Equation for a Nonlinear Harmonic Oscillator in the Extended Uncertainty Principle via the Generalized Supersymmetric Approach
摘要
In this paper, we study the exact solutions for bound states of the position-dependent mass Schrödinger equation with a nonlinear harmonic oscillator in the framework of the extended uncertainty principle by using the concept of the generalized supersymmetric approach. The bound state energy eigenvalues and the corresponding wave functions expressed in terms of modified Hermite polynomials are obtained analytically. Furthermore, special cases of interest in this problem are deduced, and our results are found to agree well with the results reported in the literature.