Marchenko inversion for perturbations. II: Inclusion of bound states. (English) Zbl 0641.35069

Aktosun, Tuncay

Inverse Probl. 3, 565-575 (1987).

[For Part I see the preceding review.]
The Marchenko inversion method of the one-dimensional non-relativistic quantum mechanics is generalized to perturbations when the bound states are present. The change in the potential that corresponds to a finite change in the scattering matrix is given as a sum of two terms. The first term, not related to the bound states, is obtained from the solution to a Marchenko equation for perturbations and the second term is related to the bound states.

MSC:

35Q99	Partial differential equations of mathematical physics and other areas of application
81U20	\(S\)-matrix theory, etc. in quantum theory
35R30	Inverse problems for PDEs
35P25	Scattering theory for PDEs

Keywords:

Marchenko inversion method; non-relativistic quantum mechanics; perturbations; bound states; potential; scattering matrix; Marchenko equation

Citations:

Zbl 0641.35068