THESIS
2019
xvi, 83 leaves : illustrations ; 30 cm
Abstract
In this thesis, we present an operator splitting method for Schrödinger equations
in the presence of electromagnetic field in the semi-classical regime. With the
operator splitting technique, the time evolution of the Schrödinger equation is
divided into two parts: the original Schrödinger equation and the convection step.
The original Schrödinger equation can be handled by the Fast Huygens Sweeping
Method(FHSM). For the convection step, we propose a semi-Lagrangian method.
We show that this method performs better than the idea of the simple extension
of the original FHSM. We also show that the convergence rate is nearly one
because of the first order splitting error. We implement this method numerically
for one dimensional, two dimensional and three dimensional cases. We a...[
Read more ]
In this thesis, we present an operator splitting method for Schrödinger equations
in the presence of electromagnetic field in the semi-classical regime. With the
operator splitting technique, the time evolution of the Schrödinger equation is
divided into two parts: the original Schrödinger equation and the convection step.
The original Schrödinger equation can be handled by the Fast Huygens Sweeping
Method(FHSM). For the convection step, we propose a semi-Lagrangian method.
We show that this method performs better than the idea of the simple extension
of the original FHSM. We also show that the convergence rate is nearly one
because of the first order splitting error. We implement this method numerically
for one dimensional, two dimensional and three dimensional cases. We also found
that this method can be applied to a time-dependent vector potential.
Post a Comment