2016/12/16 by Tamoghna Majumdar, Majumdar, Tamoghna, Maitraya Kanta Bhattacharyya +3
Engineering · Mathematics · #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Numerical methods for differential equations #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1612.05380
openalex publication_date 2016/12/16 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
In this paper, we present a simple analytical method for obtaining a nonspreading solution of the time-dependent Schrödinger equation, which is given by the Airy function. The solution is derived by imposing a restriction on the phase factor of the ansatz that is taken to solve the differential equation. Considering at first the free particle, we show that nonspreading solutions can also be obtained for a time-dependent linear potential. The method is shown to work in both one and two dimensions, and can be easily extended if required. The applicability of the method is discussed in relation to the nonlinear case.