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Dirac delta function mathematical expression proof
How do you do an integral involving the derivative of a delta function?Hamiltonian with Dirac Delta functionDirac delta function definition in scattering theoryUnfamiliar Notation in SakuraiUnderstanding Heaviside and Dirac Delta for Quantum step functionUsing Delta Dirac function as a mathematical tool in Green's functionsUnits of a dirac delta function in quantum mechanicsDelta function from poles of Green's function
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In a discussion of the second order transitions in graphene this mathematical expression is used.
$$
left|frac1varepsilon + i Gamma/2right|^2 = frac2piGammadelta(epsilon)
$$
And I'm kind of confused right now. Can someone prove this equation?
mathematical-physics mathematics dirac-delta-distributions fermis-golden-rule
edited Apr 17 at 9:33
Emilio Pisanty
91.3k23 gold badges230 silver badges475 bronze badges
asked Apr 17 at 8:20
LevonLevon
133 bronze badges
$endgroup$
add a comment
|
$begingroup$
In a discussion of the second order transitions in graphene this mathematical expression is used.
$$
left|frac1varepsilon + i Gamma/2right|^2 = frac2piGammadelta(epsilon)
$$
And I'm kind of confused right now. Can someone prove this equation?
mathematical-physics mathematics dirac-delta-distributions fermis-golden-rule
edited Apr 17 at 9:33
Emilio Pisanty
91.3k23 gold badges230 silver badges475 bronze badges
asked Apr 17 at 8:20
LevonLevon
133 bronze badges
$endgroup$
1
$begingroup$
Which discussion?
$endgroup$
– Emilio Pisanty
Apr 17 at 8:26
$begingroup$
It's about the mechanism of the 2D' peaks in graphene Raman spectrum. There the author split the second order Fermi golden rule with this equation into 4 parts.
$endgroup$
– Levon
Apr 17 at 8:38
2
$begingroup$
No, that wasn't the question. You should always provide a full bibliographic reference to the documents you're talking about.
$endgroup$
– Emilio Pisanty
Apr 17 at 9:32
add a comment
|
$begingroup$
In a discussion of the second order transitions in graphene this mathematical expression is used.
$$
left|frac1varepsilon + i Gamma/2right|^2 = frac2piGammadelta(epsilon)
$$
And I'm kind of confused right now. Can someone prove this equation?
mathematical-physics mathematics dirac-delta-distributions fermis-golden-rule
edited Apr 17 at 9:33
Emilio Pisanty
91.3k23 gold badges230 silver badges475 bronze badges
asked Apr 17 at 8:20
LevonLevon
133 bronze badges
$endgroup$
In a discussion of the second order transitions in graphene this mathematical expression is used.
$$
left|frac1varepsilon + i Gamma/2right|^2 = frac2piGammadelta(epsilon)
$$
And I'm kind of confused right now. Can someone prove this equation?
mathematical-physics mathematics dirac-delta-distributions fermis-golden-rule
mathematical-physics mathematics dirac-delta-distributions fermis-golden-rule
edited Apr 17 at 9:33
Emilio Pisanty
91.3k23 gold badges230 silver badges475 bronze badges
asked Apr 17 at 8:20
LevonLevon
133 bronze badges
edited Apr 17 at 9:33
Emilio Pisanty
91.3k23 gold badges230 silver badges475 bronze badges
asked Apr 17 at 8:20
LevonLevon
133 bronze badges
edited Apr 17 at 9:33
Emilio Pisanty
91.3k23 gold badges230 silver badges475 bronze badges
edited Apr 17 at 9:33
Emilio Pisanty
91.3k23 gold badges230 silver badges475 bronze badges
edited Apr 17 at 9:33
Emilio Pisanty
91.3k23 gold badges230 silver badges475 bronze badges
91.3k23 gold badges230 silver badges475 bronze badges
asked Apr 17 at 8:20
LevonLevon
133 bronze badges
asked Apr 17 at 8:20
LevonLevon
133 bronze badges
asked Apr 17 at 8:20
LevonLevon
133 bronze badges
133 bronze badges
1
$begingroup$
Which discussion?
$endgroup$
– Emilio Pisanty
Apr 17 at 8:26
$begingroup$
It's about the mechanism of the 2D' peaks in graphene Raman spectrum. There the author split the second order Fermi golden rule with this equation into 4 parts.
$endgroup$
– Levon
Apr 17 at 8:38
2
$begingroup$
No, that wasn't the question. You should always provide a full bibliographic reference to the documents you're talking about.
$endgroup$
– Emilio Pisanty
Apr 17 at 9:32
add a comment
|
1
$begingroup$
Which discussion?
$endgroup$
– Emilio Pisanty
Apr 17 at 8:26
$begingroup$
It's about the mechanism of the 2D' peaks in graphene Raman spectrum. There the author split the second order Fermi golden rule with this equation into 4 parts.
$endgroup$
– Levon
Apr 17 at 8:38
2
$begingroup$
No, that wasn't the question. You should always provide a full bibliographic reference to the documents you're talking about.
$endgroup$
– Emilio Pisanty
Apr 17 at 9:32
1
1
$begingroup$
Which discussion?
$endgroup$
– Emilio Pisanty
Apr 17 at 8:26
$begingroup$
Which discussion?
$endgroup$
– Emilio Pisanty
Apr 17 at 8:26
$begingroup$
It's about the mechanism of the 2D' peaks in graphene Raman spectrum. There the author split the second order Fermi golden rule with this equation into 4 parts.
$endgroup$
– Levon
Apr 17 at 8:38
$begingroup$
It's about the mechanism of the 2D' peaks in graphene Raman spectrum. There the author split the second order Fermi golden rule with this equation into 4 parts.
$endgroup$
– Levon
Apr 17 at 8:38
2
2
$begingroup$
No, that wasn't the question. You should always provide a full bibliographic reference to the documents you're talking about.
$endgroup$
– Emilio Pisanty
Apr 17 at 9:32
$begingroup$
No, that wasn't the question. You should always provide a full bibliographic reference to the documents you're talking about.
$endgroup$
– Emilio Pisanty
Apr 17 at 9:32
add a comment
|
1 Answer
1
active
oldest
votes
$begingroup$
OP's formula is derived from the Poisson kernel representation
$$ delta(varepsilon)~=~lim_Gamma to 0^+frac1pifracGamma/2varepsilon+iGamma/2 $$
of the Dirac delta distribution.
answered Apr 17 at 8:38
Qmechanic♦Qmechanic
114k13 gold badges228 silver badges1357 bronze badges
$endgroup$
add a comment
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$begingroup$
OP's formula is derived from the Poisson kernel representation
$$ delta(varepsilon)~=~lim_Gamma to 0^+frac1pifracGamma/2varepsilon+iGamma/2 $$
of the Dirac delta distribution.
answered Apr 17 at 8:38
Qmechanic♦Qmechanic
114k13 gold badges228 silver badges1357 bronze badges
$endgroup$
add a comment
|
$begingroup$
OP's formula is derived from the Poisson kernel representation
$$ delta(varepsilon)~=~lim_Gamma to 0^+frac1pifracGamma/2varepsilon+iGamma/2 $$
of the Dirac delta distribution.
answered Apr 17 at 8:38
Qmechanic♦Qmechanic
114k13 gold badges228 silver badges1357 bronze badges
$endgroup$
add a comment
|
$begingroup$
OP's formula is derived from the Poisson kernel representation
$$ delta(varepsilon)~=~lim_Gamma to 0^+frac1pifracGamma/2varepsilon+iGamma/2 $$
of the Dirac delta distribution.
answered Apr 17 at 8:38
Qmechanic♦Qmechanic
114k13 gold badges228 silver badges1357 bronze badges
$endgroup$
OP's formula is derived from the Poisson kernel representation
$$ delta(varepsilon)~=~lim_Gamma to 0^+frac1pifracGamma/2varepsilon+iGamma/2 $$
of the Dirac delta distribution.
answered Apr 17 at 8:38
Qmechanic♦Qmechanic
114k13 gold badges228 silver badges1357 bronze badges
answered Apr 17 at 8:38
Qmechanic♦Qmechanic
114k13 gold badges228 silver badges1357 bronze badges
answered Apr 17 at 8:38
Qmechanic♦Qmechanic
114k13 gold badges228 silver badges1357 bronze badges
answered Apr 17 at 8:38
Qmechanic♦Qmechanic
114k13 gold badges228 silver badges1357 bronze badges
114k13 gold badges228 silver badges1357 bronze badges
add a comment
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1
$begingroup$
Which discussion?
$endgroup$
– Emilio Pisanty
Apr 17 at 8:26
$begingroup$
It's about the mechanism of the 2D' peaks in graphene Raman spectrum. There the author split the second order Fermi golden rule with this equation into 4 parts.
$endgroup$
– Levon
Apr 17 at 8:38
2
$begingroup$
No, that wasn't the question. You should always provide a full bibliographic reference to the documents you're talking about.
$endgroup$
– Emilio Pisanty
Apr 17 at 9:32