Comment on ‘Quantum anharmonic oscillator plus delta-function potential: a molecular view of pairing formation and breaking in the coordinate space’

2021 ◽  
Vol 42 (5) ◽  
pp. 058001
Author(s):  
Francisco M Fernández
Keyword(s):  
Anharmonic Oscillator ◽  
Delta Function ◽  
Coordinate Space ◽  
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.

Finite-Range Delta-Function Potential

1959 ◽  
Vol 114 (6) ◽  
pp. 1605-1608 ◽  
Author(s):  
M. Bolsterli
Keyword(s):  
Delta Function ◽  
Finite Range ◽  
Function Potential

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.

SPACE-TIME PROPAGATION OF CONFINED GLUONS

1989 ◽  
Vol 04 (15) ◽  
pp. 3807-3818 ◽  
Author(s):  
L. S. CELENZA ◽  
C. M. SHAKIN ◽  
HUI-WEN WANG ◽  
XIN-HUA YANG
Keyword(s):  
Order Parameter ◽  
Gluon Condensate ◽  
Delta Function ◽  
Space Time ◽  
Coordinate Space ◽  
Dynamical Mass ◽  
Momentum Mode ◽  
Zero Momentum ◽  
Time Propagation

We assume that there is gluon condensate in the zero-momentum mode in the QCD ground state. A lowest-order calculation in terms of a condensate order parameter leads to a dynamical mass for gluons via the Schwinger mechanism and a gluon propagator with no on-mass-shell singularities — that is, the gluon is a "nonpropagating mode" in the gluon condensate. We transform our momentum-space propagator into coordinate space and find that the propagator has essentially the same delta-function light-cone singularities as the free propagator. However, in contrast to a theory without confinement, we show that the propagator exhibits exponential decay, both for time-like and space-like propagation. In this manner, we obtain a space-time characterization of the confinement phenomenon in terms of an order parameter of the condensate.

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