量子流體力學-理論與計算(1/2)
Date Issued
2005-07-31
Date
2005-07-31
Author(s)
楊照彥
DOI
932212E002040
Abstract
Recently, interest in the de Broglie-Bohm formulation of quantum mechanics has increased
dramatically within various fields. In the de Broglie-Bohm approach, the complex wave function is
expressed in polar form and substituted into the time-dependent linear or nonlinear Schrödinger
equation results a set of hydrodynamic-like equations which describe the flow of the probability. This
set of equations are very similar to those of classical hydrodynamics except that an additional quantum
potential term is present. The quantum potential and its associated quantum force give rise to all
quantum effects such as tunneling and interference. Despite its conceptually attractive features, there
are major computational problems inherent to the de Broglie-Bohm approach when a direct numerical
solution of the quantum hydrodynamics is attempted. In particular, the quantum potential possess
some unique features, it does not respond to the intensity of the wave but rather depends upon its form.
A desirable numerical method for solving the quantum hydrodynamics based on Schrödinger equation
not only requires high accuracy but also the ability to handle discontinuities caused by the singularity
of quantum potential. The current work has two independent directions: one is high resolution scheme,
the other is radial basis function based scheme.
Publisher
臺北市：國立臺灣大學應用力學研究所
Type
report
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