Global $\widetilde{SL(2,R)}$ representations of the Schrödinger equation with singular potential

• Autorzy: Jose Franco
• Języki publikacji: EN

Abstrakty

EN

We study the representation theory of the solution space of the one-dimensional Schrödinger equation with singular potential V λ(x) = λx −2 as a representation of $\widetilde{SL(2,\mathbb{R})}$ . The subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. By studying the subspace of K-finite vectors in this space, a distinguished family of potentials, parametrized by the triangular numbers is shown to generate a global representation of $\widetilde{SL(2,\mathbb{R})}$ ⋉ H 3, where H 3 is the three-dimensional Heisenberg group.

Słowa kluczowe

EN

Schrödinger equation; Time-dependent potentials; Lie theory; Representation theory; Globalizations

Kategorie tematyczne

• 35Q41: Time-dependent Schr\"odinger equations, Dirac equations
• 22E70: Applications of Lie groups to physics; explicit representations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 927-941

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Jose Franco

• Baylor University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0040-8