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Title:  The Bogoliubov equations and their application to a normalsuperconducting boundary 
Author(s):  Mathews, Wesley Northey 
Doctoral Committee Chair(s):  Bardeen, John 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Bogoliubov equations
normalsuperconducting boundary pair potential electron excitations 
Abstract:  The Bogo1iubov equations are used to investigate the pair potential and the electronic excitations associated with a norma1 superconducting boundary in an extreme type I superconductor, The method of the Bogoliubov equations has three advantages, for this calculation, over other methods: (1) the method offers a practical means of investigating the properties of a norma1 superconducting boundary for all temperatures below the transition temperature; (2) much of the physical insight associated with sing1eparticle wave functions can be brought to bear, and (3) the effects of non1ocality in the electrodynamics are taken into account from the outset. The foundation for the calculation is laid by a derivation and discussion of the Bogoliubov equations, in the course of which the equations are extended over the entire range of coupling strengths, Four il1ustrative examples are considered: (1) the BCS limit; (2) the normal conductorsuperconductor contact; (3) an isolated vortex line in a type II superconductor, and (4) a superconductor containing nonmagnetic impurities near the transition temperature, 1 IIn the discussion of the fourth example, the GinzburgLandau equations, for arbitrary electronic mean free path, are derived. In addition, the kernels of the GinzburgLandau theory are expressed in terms of the wave vector and frequencydependent, normal conductivity. The Bogoliubov equations are then used to work out the theory of the properties of the boundary. A method which bears an external resemblance to the standard JWKB approximation of quantum mechanics is utilized to solve the Bogoliubov equations. There is, however, an important difference: the method is capable in principle of giving exact results  the form of the eigenfunctions is not approximated. With the use of the physical picture that these solutions present local BCS states, and assuming all quantities to vary slowly over atomic distances, but permitting appreciable variations over the GinzburgLandau coherence distance, the theory of the normalsuperconducting boundary is worked out to lowest approximation. Some typical numerical results for the eigenfunctions are given. The possible improvements in and the logical extensions of the investigation are discussed. This investigation should serve as a starting point for a complete, microscopic calculation of the fundamental properties of the intermediate state. Also, the method of solution of the Bogoliubov equations should prove useful for a wide variety of problems. 
Issue Date:  1966 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/25053 
Rights Information:  Copyright 1966 Wesley Northey Mathews 
Date Available in IDEALS:  20110527 
Identifier in Online Catalog:  6127693 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois