Citation
Woodruff, Truman Owen (1955) On the orthogonalized plane wave method for calculating energy Eigenvalues in a periodic potential. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd01272004091647
Abstract
The orthogonalized plane wave OPW method is used in the first step towards determination of selfconsistent solutions of the HartreeFock equations (with Slater's freeelectron simplification of the exchange terms) for electrons in a diamondtype crystal. For illustrative purposes, the techniques developed are applied to the determination of energy eigenvalues of the valence and lowest conduction states with zero wave vector in silicon crystal. The initial crystal potential is computed from the charge distribution obtained by placing the atoms forming the crystal on the points of the appropriate space lattice. The atomic charge distributions are determined from simple orthogonalized Slater functions, which can be easily constructed for all atoms, rather than from Hartree or HartreeFock atomic functions. A procedure for determining sufficiently good approximations to the wave functions and energy eigenvalues for the core electrons in the initial crystal potential is given. The importance for the convergence and accuracy of the OPW method of using core wave functions which are eigenfunctions of the same operator used to determine the valence and excited states is emphasized. The secular determinant of the OPW method is factored by using appropriate linear combinations of orthogonalized plane waves in the trial function for the valence and excited states. In this connection a detailed exposition is given of a method for obtaining explicit representation matrices for the group of the wave vector, which can then be used to construct basis functions for these representations from sets of orthogonalized plane waves.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Physics ; energy eigenvalues 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1955 
Record Number:  CaltechETD:etd01272004091647 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd01272004091647 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  365 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  29 Jan 2004 
Last Modified:  26 Dec 2012 02:29 
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