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

Gestur Ólafsson, Shijun Zheng

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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.

Original languageAmerican English
JournalJournal of Fourier Analysis and Applications
Volume12
DOIs
StatePublished - Dec 1 2006

Disciplines

  • Education
  • Mathematics

Keywords

  • Hamiltonian
  • Poschl-Teller Potential
  • Quantum Indeterminacy
  • Quantum Mechanics
  • Schrodinger
  • Spaces

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