Abstract
Application of analytical extension of Schroedinger equation solution for quadratic singular potential and modified method of constant variation enables to construct permissible self-consistent expansions and to conduct the complete analysis of corresponding scattering problem on the whole straight line. Conservation of current density and wave function continuity when passing through x=0 singular point require the introduction of {delta}-like induced potential to Schroedinger equation. The conducted calculations show, that x{sup -2} potential can be either absolutely penetrable or absolutely opaque, depending on the choice of permissible singular corrections to the potential. The solution demonstrates the presence of latent symmetry and assumes the wide range of generalizations. 15 refs.
Citation Formats
Mineev, V S.
One-dimensional scattering problem for square singular potential; Odnomernaya zadacha rasseyaniya dlya kvadratichno singulyarnogo potentsiala.
USSR: N. p.,
1990.
Web.
Mineev, V S.
One-dimensional scattering problem for square singular potential; Odnomernaya zadacha rasseyaniya dlya kvadratichno singulyarnogo potentsiala.
USSR.
Mineev, V S.
1990.
"One-dimensional scattering problem for square singular potential; Odnomernaya zadacha rasseyaniya dlya kvadratichno singulyarnogo potentsiala."
USSR.
@misc{etde_10135905,
title = {One-dimensional scattering problem for square singular potential; Odnomernaya zadacha rasseyaniya dlya kvadratichno singulyarnogo potentsiala}
author = {Mineev, V S}
abstractNote = {Application of analytical extension of Schroedinger equation solution for quadratic singular potential and modified method of constant variation enables to construct permissible self-consistent expansions and to conduct the complete analysis of corresponding scattering problem on the whole straight line. Conservation of current density and wave function continuity when passing through x=0 singular point require the introduction of {delta}-like induced potential to Schroedinger equation. The conducted calculations show, that x{sup -2} potential can be either absolutely penetrable or absolutely opaque, depending on the choice of permissible singular corrections to the potential. The solution demonstrates the presence of latent symmetry and assumes the wide range of generalizations. 15 refs.}
place = {USSR}
year = {1990}
month = {Dec}
}
title = {One-dimensional scattering problem for square singular potential; Odnomernaya zadacha rasseyaniya dlya kvadratichno singulyarnogo potentsiala}
author = {Mineev, V S}
abstractNote = {Application of analytical extension of Schroedinger equation solution for quadratic singular potential and modified method of constant variation enables to construct permissible self-consistent expansions and to conduct the complete analysis of corresponding scattering problem on the whole straight line. Conservation of current density and wave function continuity when passing through x=0 singular point require the introduction of {delta}-like induced potential to Schroedinger equation. The conducted calculations show, that x{sup -2} potential can be either absolutely penetrable or absolutely opaque, depending on the choice of permissible singular corrections to the potential. The solution demonstrates the presence of latent symmetry and assumes the wide range of generalizations. 15 refs.}
place = {USSR}
year = {1990}
month = {Dec}
}