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.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.

American Journal of PhysicsJun 1, 199230 citations

Maximizing Time Delays for Toy Models of Quantum Scattering

Erin Crawley

We model a particle entering a complicated system from free space using an infinite chain of simple harmonic oscillators coupled to a finite, $n$ -site cluster. For a particle wavepacket with small wavenumber, an expression for the time delay in terms of the coupling strengths of the cluster is found. When the coupling strengths are varied, a minimum and maximum time delay can be found for $n=1$ . When $n=2$ , we can obtain seemingly arbitrarily large time delays. In both cases, the time delays share similarities with the time delays for the scattering from an analogous quantum well target. We conclude that this could mean that large time delays are caused by interference within the wavefunction in the target's region of space.We model a particle entering a complicated system from free space using an infinite chain of simple harmonic oscillators coupled to a finite, $n$-site cluster. For a particle wavepacket with small wavenumber, an expression for the time delay in terms of the coupling strengths of the cluster is found. When the coupling strengths are varied, a minimum and maximum time delay can be found for $n=1$. When $n=2$, we can obtain seemingly arbitrarily large time delays. In both cases, the time delays share similarities with the time delays for the scattering from an analogous quantum well target. We conclude that this could mean that large time delays are caused by interference within the wavefunction in the target's region of space.

arXiv:1812.04623Dec 11, 20180 citations

Time-delay in potential scattering theory

Arne Jensen

Communications in Mathematical PhysicsSep 1, 198158 citations

Time-delay operators in scattering theory

X.P. Wang

Jan 1, 19850 citations

Time-delay in short range potential scattering

Kalyan B. Sinha, Alok R. Mahapatra

Springer eBooksApr 7, 20080 citations

We model a particle entering a complicated system from free space using an infinite chain of simple harmonic oscillators coupled to a finite,

n

-site cluster. For a particle wavepacket with small wavenumber, an expression for the time delay in terms of the coupling strengths of the cluster is found. When the coupling strengths are varied, a minimum and maximum time delay can be found for

n=1

. When

n=2

, we can obtain seemingly arbitrarily large time delays. In both cases, the time delays share similarities with the time delays for the scattering from an analogous quantum well target. We conclude that this could mean that large time delays are caused by interference within the wavefunction in the target's region of space.