Title

Function spaces associated with Schrödinger operators: The Pöschl-Teller potential

Document Type

Article

Publication Date

12-1-2006

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 Pöschl-Teller potential. Using a dyadic system, we introduce Triebel-Lizorkin spaces and Besov 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. © Birkhauser Boston 2006.

Publication Source (Journal or Book title)

Journal of Fourier Analysis and Applications

First Page

653

Last Page

674

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