In this work, we investigate the spectrum of the non-relativistic Krönig-Penney Hamiltonian H<sub>α</sub>= -d²/dx² +αΣ<sub>m∈Z</sub>δ(-(2m+1)π) perturbed by a short-range potential λW and the spectrum of its relativistic counterpart obtained by replacing the Schrödinger Hamiltonian H<sub>α</sub> with its relativistic analogue H̅<sub>α</sub>.
The interesting feature of both spectra is that they have gaps and that bound states may occur in such gaps as a consequence of the presence of the short-range potential representing the impurity. Such bound states, often called "impurity states" in the solid state physics literature. are important with regard to the conductivity properties of solids
We show the existence of such bound states of H<sub>α</sub> + λW in each sufficiently remote gap of its essential spectrum if the integral of W is different from zero and the 1 + 𝛅-moment of W is finite for some 𝛅 > 0. Furthermore, if the potential has a constant sign we prove that there is only one bound state in each sufficiently remote gap.
We shall see that in the relativistic case one may have more than one bound state in each remote gap under the same assumptions on W. Nevertheless, we shall see that such additional bound states cannot appear in the range of energies of solid state physics. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/54524 |
| Date | January 1989 |
| Creators | Fassari, Silvestro |
| Contributors | Mathematics, Klaus, Martin, Zweifel, Paul F., Slawny, Joseph, Day, M., Polewczak, J. |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | v, 68 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 20112155 |
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