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.
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Ólafsson, G., Zheng, S. Function Spaces Associated with Schrödinger Operators: The Pöschl-Teller Potential. J Fourier Anal Appl 12, 653–674 (2006). https://doi.org/10.1007/s00041-006-6011-3
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DOI: https://doi.org/10.1007/s00041-006-6011-3