Wave packet dynamics for a non-linear Schrodinger equation: Qualitative changes with changes in the initial width

2014/12/01 by Sukla Pal, Pal, Sukla, Jayanta K. Bhattacharjee +1
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies

paper · pdf · doi:10.48550/arxiv.1412.0573

openalex publication_date 2014/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The propagation of an initially Gaussian wave packet of width Δ₀ in a cubic non-linear Schrodinger equation with a negative coupling constant for the nonlinear term is considered . It is predicted analytically and verified numerically that for a free particle if Δ₀ is less than a critical value Δ_c, then the packet will propagate in time with linearly growing width but for Δ>Δ_c, the packet will start becoming narrow and cease to be a Gaussian . For a simple harmonic oscillator, we find that for Δ₀ smaller than a critical value, there always exist a coupling strength for which the packet simply oscillates about the mean position without changing its shape.

Related

• On Solutions to the Nonlinear Phase Modification of the Schroedinger Equation
• Nonlinear, non-signaling Schrödinger equation
• Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
• Nonlinear Propagation of Coherent States through Avoided Energy Level Crossing
• The Nonlinear Schroedinger equation: solitons dynamics