Function spaces associated with Schrödinger operators: The Pöschl-Teller potential
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
Ólafsson, G., & Zheng, S. (2006). Function spaces associated with Schrödinger operators: The Pöschl-Teller potential. Journal of Fourier Analysis and Applications, 12 (6), 653-674. https://doi.org/10.1007/s00041-006-6011-3