Example12​​UniversalEquilibriuminQuantumLightTheory
​​QuantumLightTheory""hasbeenfullybasedonNewton'sThirdLaw:​​​​
n
∑
i=1
F
i
=0​​​​InQuantumLightTheory:​​​​​​TheElectricForcedensitiesonlyinteractwiththeElectricForceDensities​​ TheMagneticForcedensitiesonlyinteractwiththeMagneticForceDensities​​ TheGravitationalForceDensitiesonlyinteractwithagroupofForceDensities:​​​​1InertiaForceDensities​​2EnergyGradientForceDensities​​3GravitationalForceDensities​​​​​​​​ExampleofaLASER-BEAMwithaGaussianIntensitydivison
-K2
2
x
+
2
y

,combinedwithanarbitrarydivisiong[x,y]inthe(x,y)plane,propagatinginthez-directionwiththespeedoflightc=
1
ϵ0μ0
.
​​​
Book:
RisingoftheJamesWebbSpaceTelescopeanditsFundamentalBlindnes
:Page16,Equation(19)​​ExampleofaLASER-BEAMwithaGaussianIntensitydivison
-K2
2
x
+
2
y

,combinedwithanarbitrarydivisiong[x,y]inthe(x,y)plane,propagatinginthez-directionwiththespeedoflightc=
1
ϵ0μ0
.​​TheinputfortheElectricFieldIntensity{E(x,y,z,)=ev}andtheMagneticFieldIntensity{H(x,y,z,)=mv}hasbeensubstitutedintheFieldEquationfortheElectromagneticField(BookEquation19,page16).​​​​​​-
1
2
c
∂(
E
×
Η
)
∂ t
+
ε
0
E
(∇. 
E
) −
ε
0
E
×(∇×
E
)+
μ
0
Η
(∇. 
Η
)−
μ
0
Η
×(∇× 
Η
)Equation(19)​​​​​​Whichcanbewrittenas:​​​​term1=-
1
2
c
∂(
E
×
Η
)
∂ t
(InertiaofLight)​​​​term2=
ε
0
E
(∇. 
E
) (ElectricForceDensity) ​​​​term3=−
ε
0
E
×(∇×
E
)(MagneticForceDensitybytheLorentzTransformation""oftheElectricFieldIntensity)​​​​term4=
μ
0
Η
(∇. 
Η
)(MagneticForceDensity)​​​​term5=−
μ
0
Η
×(∇× 
Η
) (ElectricForceDensitybythe"Lorentz Transformation"oftheMagneticFieldIntensity)​​​​Equation(19)equals:​​​​term1+term2+term3+term4+term5=0
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
x=.
In[]:=
y=.
In[]:=
z=.
In[]:=
t=.
In[]:=
Get["VectorAnalysis`"]
General
:VectorAnalysis` is now obsolete. The legacy version being loaded may conflict with current functionality. See the Compatibility Guide for updating information.
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
SetCoordinates[Cartesian[x,y,z]]
Out[]=
Cartesian[x,y,z]
In[]:=
{Coordinates[Cartesian],CoordinateRanges[Cartesian]}
Out[]=
{{x,y,z},{-∞<x<∞,-∞<y<∞,-∞<z<∞}}
In[]:=
K2=.
In[]:=
f[x,y]=.
Unset
:Assignment on f for f[x,y] not found.
Out[]=
$Failed
In[]:=
ev=f[x,y]gz-
1
ϵ0
μ0
t,0,0
Out[]=
f[x,y]gz-
t
ϵ0
μ0
,0,0
In[]:=
mv=(1/Sqrt[μ0])*Sqrt[ϵ0]*​​0,f[x,y]*gz-
1
ϵ0
μ0
t,0
Out[]=
0,
ϵ0
f[x,y]gz-
t
ϵ0
μ0

μ0
,0
​
In[]:=
Div[ev]
Results for the electromagentic force densities in resp x-direction, y-direction, z-direction: