Data Processing for Corrections to the Two Potentials from the Generalized Uncertainty Principle

Various theories of Quantum Gravity predict the existence of a minimum observable length, or a maximum observable momentum, and the related generalized uncertainty principle (GUP), and it influences all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. The GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional toandrespectively, where is the GUP parameter. By considering both terms as perturbations .We compute such corrections to the two typical potentials: parabolic potential toand Dirac potential to. We show that the GUP affects reflection and transmission coefficients of the two potentials.