Zero range potential approximation in quantum scattering problems

2019 ◽  
Vol 87 (10) ◽  
pp. 796-801 ◽  
Author(s):  
Eliton Popovicz Seidel ◽  
Felipe Arretche
Keyword(s):  
Quantum Scattering ◽  
Potential Approximation ◽  
Scattering Problems ◽  
Range Potential ◽  
Zero Range

Multiphoton detachment from a zero-range potential revisited

2010 ◽  
Vol 283 (5) ◽  
pp. 850-854
Author(s):  
W. Becker ◽  
D.B. Milošević
Keyword(s):  
Range Potential ◽  
Zero Range ◽  
Multiphoton Detachment

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

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