Faculty of Physics - University of Bucharest

UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2024-11-21 20:39

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Conference: Bucharest University Faculty of Physics 2008 Meeting

Section: Theoretical Physics and Applied Mathematics Seminar

Title:

Numerical integration of TDSE in lenght gauge and velocity gauge

Authors:

Madalina Boca

Affiliation:

Faculty of Physics and Centre for Advanced Quantum Physics, University of Bucharest

E-mail

boca@barutu.fizica.unibuc.ro

Keywords:

TDSE, lenght gauge, velocity gauge

Abstract:

We focus on the problem of numerical integration of the time-dependent Schrodinger equation for an atom in a laser pulse described in the nonrelativistic dipole approximation. Although in an exact treatment both length and velocity gauges are completely equivalent, being related by a unitary transformation, numerical solutions of the same TDSE calculated in the two above mentioned gauges can be different. We integrate the time dependent Schrodinger equation for a simple one-dimensional model problem, using different numerical algorithms in both lenght and velocity gauges. By comparing the results we show that the numerical solution of the TDSE in the velocity gauge gives a better description of the wave-function at large distances, while the length gauge is more accurate near the nucleus.