In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a basis for the space of continuous functions as a subspace of L2[a,b]. A numerical method is proposed to solve for these eigenfunctions when the Hamiltonian is considered as an operator on Rn. The paper finishes with a discussion of examples of Schrödinger equations and the solutions.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc5453 |
| Date | 12 1900 |
| Creators | Kazemi, Parimah |
| Contributors | Neuberger, John W., Douglass, Matthew, Mauldin, R. Daniel |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Copyright, Kazemi, Parimah, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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