Time delay for one-dimensional quantum systems with steplike potentials

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dc.creatorAmrein, W. O.
dc.creatorJacquet, Philippe A.
dc.date2006-10-23
dc.date.accessioned2026-07-07T12:37:47Z
dc.date.available2026-07-07T12:37:47Z
dc.descriptionThis paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schrödinger Hamiltonian $H = -Δ+ V$ with a potential $V(x)$ converging to different limits $V_{\ell}$ and $V_{r}$ as $x \to -\infty$ and $x \to +\infty$ respectively. Due to the anisotropy they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V(x)$ vanishes as $|x| \to \infty$ ($V_\ell = V_r$). We show that it remains true in the anisotropic case $V_\ell \not = V_r$, i.e. we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression which is commonly used for time delay in the literature.
dc.description48 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/quant-ph/0610198
dc.identifierhttp://arxiv.org/abs/quant-ph/0610198
dc.identifierPhys.Rev.A75:022106,2007
dc.identifierdoi:10.1103/PhysRevA.75.022106
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218559
dc.subjectQuantum Physics
dc.subjectMathematical Physics
dc.titleTime delay for one-dimensional quantum systems with steplike potentials
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