Title

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

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.

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