Proof of Cramer’s rule with Dirac delta function

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.

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All about the dirac delta function(?)

Resonance ◽

10.1007/bf02866759 ◽

2003 ◽

Vol 8 (8) ◽

pp. 48-58 ◽

Cited By ~ 17

Author(s):

V Balakrishnan

Keyword(s):

Delta Function ◽

Dirac Delta Function ◽

Dirac Delta

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Spectral Distribution of the Weber Operator Perturbed by the Dirac Delta Function

Differential Equations ◽

10.1134/s0012266121080048 ◽

2021 ◽

Vol 57 (8) ◽

pp. 1003-1009

Author(s):

A. S. Pechentsov

Keyword(s):

Spectral Distribution ◽

Delta Function ◽

Dirac Delta Function ◽

Dirac Delta

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Dirac Delta Function from Closure Relation of Orthonormal Basis and its Use in Expanding Analytic Functions

Journal of Nepal Physical Society ◽

10.3126/jnphyssoc.v6i2.34872 ◽

2020 ◽

Vol 6 (2) ◽

pp. 158-163

Author(s):

B. B. Dhanuk ◽

K. Pudasainee ◽

H. P. Lamichhane ◽

R. P. Adhikari

Keyword(s):

Analytic Functions ◽

Orthonormal Basis ◽

Special Functions ◽

Single Point ◽

Functional Space ◽

Delta Function ◽

Hamiltonian Operator ◽

Dirac Delta Function ◽

Closure Relation ◽

Dirac Delta

One of revealing and widely used concepts in Physics and mathematics is the Dirac delta function. The Dirac delta function is a distribution on real lines which is zero everywhere except at a single point, where it is infinite. Dirac delta function has vital role in solving inhomogeneous differential equations. In addition, the Dirac delta functions can be used to explore harmonic information’s imbedded in the physical signals, various forms of Dirac delta function and can be constructed from the closure relation of orthonormal basis functions of functional space. Among many special functions, we have chosen the set of eigen functions of the Hamiltonian operator of harmonic oscillator and angular momentum operators for orthonormal basis. The closure relation of orthonormal functions used to construct the generator of Dirac delta function which is used to expand analytic functions log(x + 2),exp(-x2) and x within the valid region of arguments.

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