Shape Resonances: A Comparison between Parabolic and Flat Bottom Potentials

Sharp 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