Compact Operators and the Schrödinger Equation

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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.

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Kazemi, Parimah December 2006.

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  • Kazemi, Parimah

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Description

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.

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  • December 2006

Added to The UNT Digital Library

  • May 5, 2008, 3:04 p.m.

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  • June 25, 2009, 1:24 p.m.

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Kazemi, Parimah. Compact Operators and the Schrödinger Equation, thesis, December 2006; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc5453/: accessed December 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .