Squeezed-state Gaussian wave packet in a finite square well potential

Abstract

This paper investigated the squeezed-state Gaussian wave packet (SGWP) in the presence of a finite square well potential, specifically the relationship between the position uncertainty Δx and the position-momentum correlation parameter C, which is a real parameter that induces a contraction of SGWP or the temporary decrease in Δx. The time-dependent Schrödinger equation was solved numerically using the Crank-Nicolson method. The results show that: (a) a temporary contraction of SGWP occurred in the presence of the potential well for C < 0 for the cases E = V, E < V, and E > V; (b) when E ≤ V, the contraction of the reflected SGWP (inside the well) occurred for C = −5.0 and; (c) when E ≥ V, both the reflected and primary transmitted (right of the well) wave packet contracts for C = −5.0 at different durations.