Nontrivial wave-packet collision and broadening in fractional Schrodinger equation Formalism

Abstract

In this work, we study the collision of two and three Gaussian wave-packets in the fractional quantum mechanics platform. For this purpose, we study the effects of different parameters such as fractionality, nonlinear interactions, delta potential barrier height, and position, etc. on two and three wave-packet collision phenomena. We have used the split-step finite difference method to solve the space fractional Schrodinger equation. We have discussed the conditions lead to (A) wave-packet fission, (B) wave-packet fusion and (C) larger amplitude pulse generation through an inelastic collision of wave-packets. For these purposes, we have placed a defect in front of the colliding wave-packets. However, against the supercontinuum generation, we do not require huge values of nonlinearity. Besides, we have provided a phase diagram that determines the allowed defect strength and fractionality strength α to have the wave-packet fusion or fission conditions.