The inverse problem for the onedimensional Schroedinger equation with an energydependent potential, part 1
Abstract
The Schroedinger equation is considered. The energy dependence of the potential takes a certain form and belongs to a large class V of pairs of real potentials admitting no bound state. To each pair of V is associated a 2x2 matrix valued function shown to be the scattering matrix. Its real part is identified with the physical part of the scattering problem while the complex part of the scattering matrix is identified with the reflection coefficient to the right. Both real and complex parts are shown to belong to classes S and R the properties of which are given. Two systems of integrodifferential equations are derived connecting quantities related to the real and complex part of the scattering matrix.
 Publication:

Unknown
 Pub Date:
 January 1975
 Bibcode:
 1975ipod.reptQ....J
 Keywords:

 Integral Equations;
 S Matrix Theory;
 Schroedinger Equation;
 Theorem Proving;
 Wave Reflection;
 Asymptotic Methods;
 Functionals;
 Potential Energy;
 Potential Fields;
 Uniqueness Theorem;
 Wave Scattering;
 Nuclear and HighEnergy Physics