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Global SL(2,R) representations of the Schrödinger equation with time-dependent potentials.

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dc.contributor.advisor Sepanski, Mark R. (Mark Roger)
dc.contributor.author Franco, Jose A.
dc.date.copyright 2012-05
dc.identifier.uri http://hdl.handle.net/2104/8428
dc.description.abstract We study the representation theory of the solution space of the one-dimensional Schrödinger equation with time-dependent potentials that possess sl₂-symmetry. We give explicit local intertwining maps to multiplier representations and show that the study of the solution space for potentials of the form V (t, x) = g₂(t)x²+g₁(t)x+g₀ (t) reduces to the study of the potential free case. We also show that the study of the time-dependent potentials of the form V (t, x) = λx⁻² + g₂(t)x² + g₀(t) reduces to the study of the potential V (t, x) = λx⁻². Therefore, we study the representation theory associated to solutions of the Schrödinger equation with this potential only. The subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. en_US
dc.publisher en
dc.rights Baylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission. en_US
dc.subject Representation theory. en_US
dc.title Global SL(2,R) representations of the Schrödinger equation with time-dependent potentials. en_US
dc.type Thesis en_US
dc.description.degree Ph.D. en_US
dc.rights.accessrights Worldwide access. en_US
dc.rights.accessrights Access changed 1/13/14.
dc.contributor.department Mathematics.
dc.contributor.schools Baylor University. Dept. of Mathematics. en_US


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