After an introduction to the variational principle of three body systems via the Helium atom, we present general analytical formulas for the radial parts of integrals that occur when three body systems are described using wave functions that consist of powers and exponentials in all three interparticle Hylleraas coordinates [Hylleraas1929]. This work is an extension of integrals given by Harris, Frolov and Smith, Jr. [Harris2004]. Specifically included are radial integrals encountered in calculations involving the dipole moment matrix element in Hylleraas coordinates that contain a function f(kr 1) (such as a spherical Bessel function) in addition to a plane wave, a hydrogenic orbital and exponentials in all three interparticle coordinates.
|Advisor:||Straton, Jack C.|
|Commitee:||La Rosa, Andres, Leung, Peter|
|School:||Portland State University|
|School Location:||United States -- Oregon|
|Source:||MAI 55/03M(E), Masters Abstracts International|
|Subjects:||Quantum physics, Physics, Particle physics|
|Keywords:||Analytical formulas, Dipole transition, Ground state wavefunctions, Hylleraas coordinates, Photodetachment, Spherical bessel function|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be