Supersymmetry in Quantum Mechanics by Generalized Uncertainty Principle

Abstract

In this paper, we study supersymmetry in quantum mechanics using the generalized uncertainty principle (GUP), or in other words, generalized supersymmetry in quantum mechanics. We construct supersymmetry in the generalized form of the momentum operator, which is derived from GUP. By generalizing the creation and annihilation operators, we can transform the supersymmetry into a generalized state. In the following, we address the challenge of solving the Schr\"odinger equation for the generalized Hamiltonian. To overcome this difficulty, we employ perturbation theory to establish a relationship between the creation and annihilation operators. By solving this equation analytically and utilizing wave functions and energy levels, we can generate new potentials using the creation and annihilation operators of the wave functions and energy levels for the newer potentials.