scholarly journals On the direct and inverse transmission eigenvalue problems for the Schrödinger operator on the half line

2020 ◽  
Vol 43 (15) ◽  
pp. 8434-8448 ◽  
Author(s):  
Xiao‐Chuan Xu
Keyword(s):  
Schrödinger Operator ◽  
Eigenvalue Problems ◽  
Half Line ◽  
Schrodinger Operator ◽  
Transmission Eigenvalue

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‖.

Sign in / Sign up

Export Citation Format

Share Document