Scattering and Bound States in One-Dimensional Potential

Wang Zhi-liang

One-dimensional δ-potential well bound state and one-dimensional δ-scattering potential were discussed by Schrdinger and Heisenberg representation in the wave function in the time-dependent state.It is proved more generally that one-dimensional δ-potential well restraint level is the δ-barrier scattering amplitude pole.

A. Ronveaux

Natalia Shypka, Orest Hryhorchak, V. Pastukhov

We consider bound and scattering states of the one-dimensional dimer formed by two coupled non-identical atoms when one of them also interacts with the zero-range potential located at the origin. By calculating the dimer localized and scattering wave functions, we identify properties of the system without the two-body bound-state breakdown. In general, we predict an enhancement of the dimer reflection compared to a single atom, except for a narrow region on the attractive side of the external potential.

S. Brandt, Hans Dieter Dahmen

W. van Dijk, Ken Kiers A

The time delay or the time advance in the scattering of simple one-dimensional systems can be evaluated in a straightforward manner for certain potential models. It is found that when the interacting potential is attractive and has a strength such that it nearly supports an additional bound state, the time delay at small scattering energy is very large. On the other hand, if the potential supports a bound state with nearly zero binding energy, the time advance near threshold is anomalously large. The behavior of a wave packet scattering from the double delta-function potential is also investigated.

S. Brandt, Hans Dieter Dahmen