Transport approach to one‐dimensional quantum scattering

1977 ◽  
Vol 45 (11) ◽  
pp. 1091-1093 ◽  
Author(s):  
Yoel Tikochinsky
Keyword(s):  
Quantum Scattering ◽  
One Dimensional ◽  
Transport Approach

scholarly journals Quantum scattering in quasi-one-dimensional cylindrical confinement

2005 ◽  
Vol 72 (4) ◽  
Author(s):  
J. I. Kim ◽  
J. Schmiedmayer ◽  
P. Schmelcher
Keyword(s):  
Quantum Scattering ◽  
One Dimensional

On quantum scattering by δ'(x)} and quasi δ'(x) distributions

2007 ◽  
Vol 85 (9) ◽  
pp. 967-979
Author(s):  
R K Dubey ◽  
V J Menon ◽  
M K Pandey ◽  
D N Tripathi
Keyword(s):  
Quantum Scattering ◽  
Length Scale ◽  
Range Interaction ◽  
One Dimensional ◽  
Transmission Amplitude ◽  
Reflection Amplitude ◽  
Scattering Wave ◽  
Zero Range ◽  
Ordinary Point ◽  
The One

The zero-range interaction U(x) occurring in the one-dimensional, time-independent Schrödinger equation is regarded as a smoothed distribution characterized by a tiny length scale b such that the origin becomes an ordinary point. A neighbourhood around the origin is scanned by defining inner demarcation points a±≡ ±b/N and outer demarcation points b±≡ ±Nb with N >> 1. Then a sequence of simple Lemmas permits (i) construction of a systematic procedure for simultaneously solving the scattering wave function ψ(0) at the origin, its derivative ψ'(0) there, the transmission amplitude B, as well as the reflection amplitude D; and (ii) unambiguous application to scattering by the previously known δ'(x) and newly proposed quasi δ'(x) potentials in the Cauchy representation of various distributions.PACS No.: 03.65.Nk

Wronskian method for one-dimensional quantum scattering

2011 ◽  
Vol 79 (8) ◽  
pp. 877-881 ◽  
Author(s):  
Francisco M. Fernández
Keyword(s):  
Quantum Scattering ◽  
One Dimensional

scholarly journals TIME DELAY FOR DISPERSIVE SYSTEMS IN QUANTUM SCATTERING THEORY

2009 ◽  
Vol 21 (05) ◽  
pp. 675-708 ◽  
Author(s):  
RAFAEL TIEDRA DE ALDECOA
Keyword(s):  
Time Delay ◽  
Scattering Theory ◽  
Integral Formula ◽  
Radial Component ◽  
Quantum Scattering ◽  
Scattering Operator ◽  
Localization Operators ◽  
Quantum Scattering Theory ◽  
One Dimensional ◽  
Klein Gordon

We consider time delay and symmetrized time delay (defined in terms of sojourn times) for quantum scattering pairs {H0 = h(P), H}, where h(P) is a dispersive operator of hypoelliptic-type. For instance, h(P) can be one of the usual elliptic operators such as the Schrödinger operator h(P) = P2 or the square-root Klein–Gordon operator [Formula: see text]. We show under general conditions that the symmetrized time delay exists for all smooth even localization functions. It is equal to the Eisenbud–Wigner time delay plus a contribution due to the non-radial component of the localization function. If the scattering operator S commutes with some function of the velocity operator ∇h(P), then the time delay also exists and is equal to the symmetrized time delay. As an illustration of our results, we consider the case of a one-dimensional Friedrichs Hamiltonian perturbed by a finite rank potential. Our study puts into evidence an integral formula relating the operator of differentiation with respect to the kinetic energy h(P) to the time evolution of localization operators.

scholarly journals DEVELOPMENT AND NUMERICAL ANALYSIS OF "BLACK-BOX" COUNTERPROPAGATING WAVE ALGORITHM FOR EXACT QUANTUM SCATTERING CALCULATIONS

2007 ◽  
Vol 06 (01) ◽  
pp. 99-125 ◽  
Author(s):  
BILL POIRIER
Keyword(s):  
Dynamical System ◽  
Numerical Analysis ◽  
Bound States ◽  
Black Box ◽  
Quantum Scattering ◽  
Quantum Trajectories ◽  
One Dimensional ◽  
Quantum Dynamical ◽  
The One ◽  
Wave Decomposition

In a recent series of papers,1-3 a bipolar counter-propagating wave decomposition, Ψ = Ψ+ + Ψ-, was presented for stationary bound states Ψ of the one-dimensional Schrödinger equation, such that the components Ψ± approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Ψ has many nodes, or is wildly oscillatory. In this paper, the earlier results are used to construct an universal "black-box" algorithm, numerically robust, stable and efficient, for computing accurate scattering quantities of any quantum dynamical system in one degree of freedom.

One‐dimensional quantum scattering in an eigendifferential basis

1984 ◽  
Vol 52 (5) ◽  
pp. 443-445 ◽  
Author(s):  
Lawrence L. Halcomb ◽  
Dennis J. Diestler
Keyword(s):  
Quantum Scattering ◽  
One Dimensional
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