The scattering and shrinking of a Gaussian wave packet by delta function potentials
Name
836717447-MIT.pdf
Description
Full printable version
Size
4.88 MB
Format
Adobe PDF
Checksum (MD5)
0488336831793205271268b0d10043c9
Author(s)
Sun, Fei, S.B. Massachusetts Institute of Technology
Advisor(s)
Edmund Bertschinger.
Date Issued
2012
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we wish to test the hypothesis that scattering by a random potential causes localization of wave functions, and that this localization is governed by the Born postulate of quantum mechanics. We begin with a simple model system: a one-dimensional Gaussian wave packet incident from the left onto a delta function potential with a single scattering center. Then we proceed to study the more complicated models with double and triple scattering centers. Chapter 1 briefly describes the motivations behind this thesis and the phenomenon related to this research. Chapter 2 to Chapter 4 give the detailed calculations involved in the single, double and triple scattering cases; for each case, we work out the exact expressions of wave functions, write computer programs to numerically calculate the behavior of the wave packets, and use graphs to illustrate the results of the calculations. In Chapter 5, we study the parameters that determine how much the wave function shrinks, including the initial width, the initial position and the momentum of the Gaussian wave packet, and the strength of and the spacing between the delta functions; then we examine different combinations of the parameters in order to find a pattern to achieve maximum shrinking. Chapter 6 concludes the thesis with the essential results of this research as well as its implications and potentials.
Description
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 59).
Subjects
Physics.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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