Proper treatment of the delta function potential in the one‐dimensional Dirac equation

1987 ◽  
Vol 55 (8) ◽  
pp. 737-739 ◽  
Author(s):  
M. G. Calkin ◽  
D. Kiang ◽  
Y. Nogami
Keyword(s):  
Dirac Equation ◽  
Delta Function ◽  
Proper Treatment ◽  
One Dimensional ◽  
The One ◽  
Function Potential

scholarly journals TRANSMISSION PROPERTIES OF THE ONE-DIMENSIONAL ARRAY OF DELTA POTENTIALS

2011 ◽  
Vol 25 (16) ◽  
pp. 1349-1358 ◽  
Author(s):  
GUILLERMO CORDOURIER-MARURI ◽  
ROMEO DE COSS ◽  
VIRENDRA GUPTA
Keyword(s):  
Linear Array ◽  
Delta Function ◽  
Transmission Probability ◽  
Quantum Waveguide ◽  
One Dimensional ◽  
Transmission Properties ◽  
Moving Particle ◽  
The One ◽  
Regular Arrays ◽  
Function Potential

The problem of one-dimensional quantum wire along which a moving particle interacts with a linear array of N delta-function potentials is studied. Using a quantum waveguide approach, the transfer matrix is calculated to obtain the transmission probability of the particle. Results for arbitrary N and for specific regular arrays are presented. Some particular symmetries and invariances of the delta-function potential array for the N = 2 case are analyzed in detail. It is shown that perfect transmission can take place in a variety of situations.

scholarly journals Intertwining technique for the one-dimensional stationary Dirac equation

2003 ◽  
Vol 305 (2) ◽  
pp. 151-189 ◽  
Author(s):  
L.M. Nieto ◽  
A.A. Pecheritsin ◽  
Boris F. Samsonov
Keyword(s):  
Dirac Equation ◽  
One Dimensional ◽  
The One ◽  
Stationary Dirac Equation

Unilateral Global Bifurcation from Infinity in Nonlinearizable One-Dimensional Dirac Problems

2021 ◽  
Vol 31 (01) ◽  
pp. 2150005
Author(s):  
Ziyatkhan S. Aliyev ◽  
Nazim A. Neymatov ◽  
Humay Sh. Rzayeva
Keyword(s):  
Dirac Equation ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nontrivial Solutions ◽  
One Dimensional ◽  
Bifurcation From Infinity ◽  
The One ◽  
Nodal Properties

In this paper, we study the unilateral global bifurcation from infinity in nonlinearizable eigenvalue problems for the one-dimensional Dirac equation. We show the existence of two families of unbounded continua of the set of nontrivial solutions emanating from asymptotically bifurcation intervals and having the usual nodal properties near these intervals.

scholarly journals FERMIONIC DUAL OF ONE-DIMENSIONAL BOSONIC PARTICLES WITH DERIVATIVE DELTA FUNCTION POTENTIAL

2010 ◽  
Vol 25 (09) ◽  
pp. 715-725
Author(s):  
B. BASU-MALLICK ◽  
TANAYA BHATTACHARYYA
Keyword(s):  
Center Of Mass ◽  
Delta Function ◽  
Bose Gas ◽  
Duality Relation ◽  
Coupling Constant ◽  
Range Interaction ◽  
Fermionic System ◽  
One Dimensional ◽  
Zero Range ◽  
Function Potential

We investigate the boson–fermion duality relation for the case of quantum integrable derivative δ-function Bose gas. In particular, we find a dual fermionic system with nonvanishing zero-range interaction for the simplest case of two bosonic particles with derivative δ-function interaction. The coupling constant of this dual fermionic system becomes inversely proportional to the product of the coupling constant of its bosonic counterpart and the center-of-mass momentum of the corresponding eigenfunction.

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