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Numerical solution of the time‐dependent Schrödinger equation for continuum states
Author(s) -
Ritchie Burke,
Weatherford Charles A.
Publication year - 2000
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/1097-461x(2000)80:4/5<934::aid-qua42>3.0.co;2-o
Subject(s) - wave packet , bounded function , schrödinger equation , grid , scattering , fourier transform , physics , boundary (topology) , fast fourier transform , boundary value problem , positronium , mathematical analysis , wave equation , mathematics , quantum mechanics , electron , positron , geometry , algorithm
The time‐dependent Schrödinger equation is solved numerically by using fast‐Fourier transforms (FFTs) to evaluate the integrating factor e ( i /2)∇ 2 ( t − t ′)in the integral form of the Schrödinger equation. The need for boundary conditions at grid boundaries is obviated provided the grid box is large enough that V Ψ, on which the integrating factor operates, is bounded within it. This means that Ψ can be represented as appropriately unbounded rather than as a wave packet confined within the box, whose spreading over time to the grid boundaries places practical limits on the duration of the collision. This development means that numerical simulations for electron or positron scattering can be carried out at lower momenta k <1 than is currently practical using a wave packet description. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 934–941, 2000