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On the continuity of the reflection coefficient of one-dimensional Schrödinger equation. (Russian) Zbl 0644.34014

The scalar Schrödinger equation \(-y''(x)+q(x)y(x)=k^ 2y(x),\) \(x\in R^ 1\) (*) \(\int^{\infty}_{-\infty}(1+| x|)| q(x)| dx<\infty\) has special solutions \[ f(x,k)=\exp (\pm ikx)\pm \int^{\pm \infty}_{x}C\sigma^{\pm}(\frac{x+t}{2})\exp (\pm ikt)dt \] where \(\sigma^{\pm}(x)=\pm \int^{\pm \infty}_{x}| q(t)| dt.\) Using \(f_{\pm}(x,k)\) the reflexion coefficient \(r^+(k)\) can be defined. The author discusses the continuity of \(r^+(k)\) when \(k\to 0\) and (*) is satisfied.
Reviewer: T.Dłotko

MSC:

34A99 General theory for ordinary differential equations
35J10 Schrödinger operator, Schrödinger equation
70B05 Kinematics of a particle
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