Function Spaces Associated with Schrödinger Operators: The Pöschl-Teller Potential

Authors

Gestur Olafsson, Louisiana State University at Baton RougeFollow
Shijun Zheng, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

12-2006

Publication Title

Journal of Fourier Analysis and Applications

DOI

10.1007/s00041-006-6011-3

ISSN

1531-5851

Abstract

We address the function space theory associated with the Schrödinger operator H = −d²/dx²+V . The discussion is featured with potential V (x) = −n(n+1) sech²x, which is called in quantum physics the Pöschl-Teller potential. Using biorthogonal dyadic system, we introduce Besov spaces and Triebel-Lizorkin spaces (including Sobolev spaces) associated with H. We then use interpolation method to identify these spaces with the classical ones for a certain range of p, q > 1. A physical implication is that the corresponding wave function ψ(t, x) = e^-itHf(x) admits appropriate time decay in the Besov space scale.

Recommended Citation

Olafsson, Gestur, Shijun Zheng. 2006. "Function Spaces Associated with Schrödinger Operators: The Pöschl-Teller Potential." Journal of Fourier Analysis and Applications, 12 (6): 653-674. doi: 10.1007/s00041-006-6011-3
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/694