Schrödinger equation and resonant scattering in the presence of a minimal length

In this work we have studied the consequences of the minimal length, which arises in many theories of quantum gravity, on the Scattering of a point particle by a spherically symmetric potential. The modified Schrödinger equation is factorized to be of second order in position space representation. For the square well potential analytic expressions for the scattering states are obtained. Then the phase shifts are deduced. It is shown that the minimal length has two effects on the resonant scattering. The first one is that the minimal length increases slightly the resonant cross section and the second is the shift of the position of the resonances.