Analytic continuation and asymptotic behavior in angular momentum of the scattering matrix in potential scattering

1963 ◽  
Vol 28 (1) ◽  
pp. 66-77 ◽  
Author(s):  
F. Calogero
Keyword(s):  
Asymptotic Behavior ◽  
Angular Momentum ◽  
Analytic Continuation ◽  
Scattering Matrix ◽  
Potential Scattering

scholarly journals Generalized eigenfunctions for quantum walks via path counting approach

2021 ◽  
pp. 2150019
Author(s):  
Takashi Komatsu ◽  
Norio Konno ◽  
Hisashi Morioka ◽  
Etsuo Segawa
Keyword(s):  
Asymptotic Behavior ◽  
Quantum Walk ◽  
Scattering Matrix ◽  
Quantum Walks ◽  
Tunneling Effect ◽  
Counting Approach ◽  
Finite Rank Perturbation ◽  
Generalized Eigenfunctions ◽  
The Green Function ◽  
Path Counting

We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-dependent quantum walk naturally appears in the asymptotic behavior at the spatial infinity of generalized eigenfunctions. The asymptotic behavior of generalized eigenfunctions is a consequence of an explicit expression of the Green function associated with the free quantum walk. When the position-dependent quantum walk is a finite rank perturbation of the free quantum walk, we derive a kind of combinatorial construction of the scattering matrix by counting paths of quantum walkers. We also mention some remarks on the tunneling effect.

Fredholm method in potential scattering and applications to complex angular momentum

1963 ◽  
Vol 23 (2) ◽  
pp. 187-220 ◽  
Author(s):  
Lowell Brown ◽  
Daniel I Fivel ◽  
Benjamin W Lee ◽  
Raymond F Sawyer
Keyword(s):  
Angular Momentum ◽  
Potential Scattering ◽  
Complex Angular Momentum

On angular momentum analyticity in hard core potential scattering

1963 ◽  
Vol 4 (4) ◽  
pp. 218-219 ◽  
Author(s):  
O. Brander
Keyword(s):  
Angular Momentum ◽  
Hard Core ◽  
Potential Scattering ◽  
Core Potential

On the uniqueness of the analytic continuation of theS matrix in angular momentum

1962 ◽  
Vol 24 (5) ◽  
pp. 957-962 ◽  
Author(s):  
G. M. Prosperi
Keyword(s):  
Angular Momentum ◽  
Analytic Continuation ◽  
Thes Matrix

Potential scattering for complex energy and angular momentum

1962 ◽  
Vol 23 (6) ◽  
pp. 954-1004 ◽  
Author(s):  
A. Bottino ◽  
A. M. Longoni ◽  
T. Regge
Keyword(s):  
Angular Momentum ◽  
Potential Scattering ◽  
Complex Energy
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