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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2012

Author dc:creator

• Franco, Jose A.

Advisor dc:contributor.advisor

• Sepanski, Mark R. (Mark Roger)

• Representation theory.

Statement dc:rights

• Baylor University works 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 libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/8428

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/8428