Shape Resonances: A Comparison between Parabolic and Flat Bottom Potentials
- Pravica, David W.
DOIAbstract
AbstractSharp exponential bounds are obtained for resonance statesψand complex eigenvalueszfor the Schrödinger equationHλψ≡(−d2/dx2+λV)ψ=zψon [0, ∞). In a compact regionV(x) is either a square-well or a parabolic potential. Asx→∞,V(x)∼V∞+VMx−μfor someμ>0. The three casesV∞<0,V∞=0 and 0<V∞<VMare considered. Results are used to studythe stratified wave propagator K=−c2(|y|)(Δx+Δy). Depending on the shape of the velocity functionc(s), resonances ofKare shown to exist
Add to ORKG