Se p 20 05 FUNCTION SPACES ASSOCIATED WITH SCHRÖDINGER OPERATORS : THE PÖSCHL - TELLER POTENTIAL

Abstract. We address the function space theory associated with the Schrödinger operatorH = −d2/dx2+V . The discussion is featured with potential V (x) = −λ(λ−1) sechx, 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) = ef(x) admits appropriate time decay in the Besov space scale.