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dc.contributor.advisorSepanski, Mark R. (Mark Roger)
dc.contributor.authorFranco, Jose A.
dc.date.accessioned2012-08-08T15:51:49Z
dc.date.available2012-08-08T15:51:49Z
dc.date.copyright2012-05
dc.date.issued2012-08-08
dc.identifier.urihttp://hdl.handle.net/2104/8428
dc.description.abstractWe 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.language.isoen_USen_US
dc.publisheren
dc.rightsBaylor 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.subjectRepresentation theory.en_US
dc.titleGlobal SL(2,R) representations of the Schrödinger equation with time-dependent potentials.en_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.rights.accessrightsWorldwide access.en_US
dc.rights.accessrightsAccess changed 1/13/14.
dc.contributor.departmentMathematics.
dc.contributor.schoolsBaylor University. Dept. of Mathematics.en_US


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