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

Franco, Jose A.

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

dc.contributor.advisor	Sepanski, Mark R. (Mark Roger)
dc.contributor.author	Franco, Jose A.
dc.contributor.department	Mathematics.
dc.contributor.schools	Baylor University. Dept. of Mathematics.	en_US
dc.date.accessioned	2012-08-08T15:51:49Z
dc.date.available	2012-08-08T15:51:49Z
dc.date.copyright	2012-05
dc.date.issued	2012-08-08
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.description.degree	Ph.D.	en_US
dc.identifier.uri	http://hdl.handle.net/2104/8428
dc.language.iso	en_US	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.rights.accessrights	Worldwide access.	en_US
dc.rights.accessrights	Access changed 1/13/14.
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