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 language | American English |
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Journal | Journal of Fourier Analysis and Applications |
Volume | 12 |
DOIs | |
State | Published - Dec 1 2006 |
Disciplines
- Education
- Mathematics
Keywords
- Hamiltonian
- Poschl-Teller Potential
- Quantum Indeterminacy
- Quantum Mechanics
- Schrodinger
- Spaces