Generalized Uncertainty Principle and Delta-Function Potential

Abstract

In recent studies, the Heisenberg uncertainty principle has been modified into the generalized uncertainty principle (GUP) to explain gravity from a quantum mechanical perspective. Here, we study the GUP corrections to the bound-state energy eigenvalues for a delta-function potential well and a double delta-function potential well using nonrelativistic quantum mechanical tools. Transmission probabilities for scattering states have also been derived and compared with the unmodified cases for both systems.