scholarly journals Small-energy analysis for the selfadjoint matrix Schrödinger operator on the half line. II

2014 ◽  
Vol 55 (3) ◽  
pp. 032103 ◽  
Author(s):  
Tuncay Aktosun ◽  
Martin Klaus ◽  
Ricardo Weder
Keyword(s):  
Schrödinger Operator ◽  
Energy Analysis ◽  
Half Line ◽  
Schrodinger Operator ◽  
Small Energy

EXISTENCE OF ALMOST EXPONENTIALLY DECAYING STATES FOR BARRIER POTENTIALS

2001 ◽  
Vol 13 (03) ◽  
pp. 267-305 ◽  
Author(s):  
RICHARD LAVINE
Keyword(s):  
Error Estimate ◽  
Half Plane ◽  
Imaginary Part ◽  
Schrödinger Operator ◽  
Small Error ◽  
Lower Half ◽  
Half Line ◽  
Schrodinger Operator ◽  
Lower Half Plane ◽  
Decaying States

For a Schrödinger operator H on the half line whose potential has a trapping barrier, and is convex outside the barrier, there exists a φ, supported mostly inside the barrier, such that for t>0, <φ, e-iHtφ>~e-izt up to a small error, where φ is obtained by cutting off a nonnormalizable solution ψ of Hψ=zψ, and z is in the lower half-plane. The imaginary part of z is estimated explicitly, and the error estimate is explicitly proportional to | Im z log | Im z‖.

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