scholarly journals Unusual situations that arise with the Dirac delta function and its derivative

2009 ◽  
Vol 31 (4) ◽  
pp. 4302-4308 ◽  
Author(s):  
F.A.B Coutinho ◽  
Y Nogami ◽  
F.M Toyama
Keyword(s):  
Quantum Mechanics ◽  
Delta Function ◽  
Dirac Delta Function ◽  
One Dimensional ◽  
Dirac Delta ◽  
Underlying Mechanisms ◽  
Usual Formula

There is a situation such that, when a function ƒ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">) is combined with the Dirac delta function δ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), the usual formula <img src="/img/revistas/rbef/v31n4/a04form01.gif" align="absmiddle">does not hold. A similar situation may also be encountered with the derivative of the delta function δ'(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), regarding the validity of <img src="/img/revistas/rbef/v31n4/a04form02.gif" align="absmiddle">. We present an overview of such unusual situations and elucidate their underlying mechanisms. We discuss implications of the situations regarding the transmission-reflection problem of one-dimensional quantum mechanics.

scholarly journals Quantum mechanics of a free particle from properties of the Dirac delta function

2011 ◽  
Vol 79 (4) ◽  
pp. 392-394 ◽  
Author(s):  
Denys I. Bondar ◽  
Robert R. Lompay ◽  
Wing-Ki Liu
Keyword(s):  
Quantum Mechanics ◽  
Free Particle ◽  
Delta Function ◽  
Dirac Delta Function ◽  
Dirac Delta

Construction of Dirac Delta Function from the Discrete Orthonormal Basis of the Function Space

2017 ◽  
pp. 54-57
Author(s):  
Hari Prasad Lamichhane
Keyword(s):  
Function Space ◽  
Orthonormal Basis ◽  
Delta Function ◽  
Hamiltonian Operator ◽  
Dirac Delta Function ◽  
Basis Set ◽  
One Dimensional ◽  
Dirac Delta ◽  
Simple Basis ◽  
Infinite Potential Well

Orthonormal basis of the function space can be used to construct Dirac delta function. In particular, set of eigenfunctions of the Hamiltonian operator of a particle in one dimensional infinite potential well forms a non-degenerate discrete orthonormal basis of the function space. Such a simple basis set is suitable to study closure property of the basis and various properties of Dirac delta function in Physics graduate lab.The Himalayan Physics Vol. 6 & 7, April 2017 (54-57)

Dirac delta regularization

2020 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Delta Function ◽  
Dirac Delta Function ◽  
Dirac Delta ◽  
Finite Result

I present a finite result for the Dirac delta "function."

scholarly journals Electromagnetic Waves Through Disordered Systems: Comparison of Intensity, Transmission and Conductance

2001 ◽  
Vol 694 ◽  
Author(s):  
Fredy R Zypman ◽  
Gabriel Cwilich
Keyword(s):  
Probability Distribution ◽  
Disordered Systems ◽  
Electromagnetic Waves ◽  
Delta Function ◽  
Rayleigh Distribution ◽  
Dirac Delta Function ◽  
Universal Form ◽  
Dirac Delta ◽  
Diffusive Regime ◽  
Analytical Expressions

AbstractWe obtain the statistics of the intensity, transmission and conductance for scalar electromagnetic waves propagating through a disordered collection of scatterers. Our results show that the probability distribution for these quantities x, follow a universal form, YU(x) = xne−xμ. This family of functions includes the Rayleigh distribution (when α=0, μ=1) and the Dirac delta function (α →+ ∞), which are the expressions for intensity and transmission in the diffusive regime neglecting correlations. Finally, we find simple analytical expressions for the nth moment of the distributions and for to the ratio of the moments of the intensity and transmission, which generalizes the n! result valid in the previous case.

All about the dirac delta function(?)

Resonance ◽  
2003 ◽  
Vol 8 (8) ◽  
pp. 48-58 ◽  
Author(s):  
V Balakrishnan
Keyword(s):  
Delta Function ◽  
Dirac Delta Function ◽  
Dirac Delta
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