Phase Shifts for Scattering by a One-Dimensional Delta-Function Potential

1969 ◽  
Vol 37 (9) ◽  
pp. 930-931 ◽  
Author(s):  
I. Richard Lapidus
Keyword(s):  
Delta Function ◽  
Phase Shifts ◽  
One Dimensional ◽  
Function Potential

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.

scholarly journals Generalized Continuity Equation for Quasi-Hermitian Hamiltonians

10.14311/1803 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Amine B. Hammou
Keyword(s):  
Continuity Equation ◽  
Delta Function ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Generalized Continuity ◽  
Unitarity Relation ◽  
Function Potential

The continuity relation is generalized to quasi-Hermitian one-dimensional Hamiltonians. As an application we show that the reflection and transmission coefficients computed with the generalized current obey the conventional unitarity relation for the continuous double delta function potential.

STRINGS COMPLETE THE SPECTRUM OF 1-D δ-FUNCTION FERMIONS

1993 ◽  
Vol 07 (10) ◽  
pp. 689-698 ◽  
Author(s):  
ERIC D. WILLIAMS
Keyword(s):  
Bethe Ansatz ◽  
Bound States ◽  
Delta Function ◽  
One Dimensional ◽  
Nested Bethe Ansatz ◽  
Function Potential

We study the completeness of the nested Bethe ansatz eigenfunctions for a one dimensional gas of spin-1/2 fermions interacting via a repulsive delta-function potential. We show the completeness of the eigenfunctions for a system in an infinite box with N fermions and the orientation of either one or two of the spins differing from the rest. This demonstrates that the spin bound states (also called Λ-strings) are necessary for completeness of the spectrum.

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.

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