Wolfram Cloud Document

Needs["NumericalCalculus`"]D0Δ=1;

x

0

=-100000;

b

0

=

1

4

2

π

Δ

;α[k_,v_]=-

v

4k

;

R

11

[k_,v_]=-

α[k,v]

2+α[k,v]

;

R

11

[k_,v_]=-

α[k,v]

2+α[k,v]

;

R

22

[k_,v_]=

α[k,v]

2-α[k,v]

;∅[k_]=

1

4

2

π

Δ

Exp[-

2

Δ

2

(k-

b

0

)

-(k-

b

0

)

x

0

];M[v_]=12NIntegrate[

2

Abs[∅[k]]

(

2

Abs[

R

11

[k,v]]

+

2

Abs[

R

22

[k,v]]

),{k,0,100000}];

ρ

11

[v]=M[v]NIntegrate[

2

Abs[

R

11

[k,v]]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

14

[v]=M[v]NIntegrate[

2

Abs[

R

11

[k,v]]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

41

[v]=M[v]NIntegrate[

2

Abs[

R

11

[k,v]]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

44

[v]=M[v]NIntegrate[

2

Abs[

R

11

[k,v]]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

12

[v]=M[v]NIntegrate[

R

11

[k,v]



R

22

[k,v]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

13

[v]=M[v]NIntegrate[

R

11

[k,v]



R

22

[k,v]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

42

[v]=M[v]NIntegrate[

R

11

[k,v]



R

22

[k,v]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

43

[v]=M[v]NIntegrate[

R

11

[k,v]



R

22

[k,v]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

21

[v]=M[v]NIntegrate[



R

11

[k,v]

R

22

[k,v]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

31

[v]=M[v]NIntegrate[



R

11

[k,v]

R

22

[k,v]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

24

[v]=M[v]NIntegrate[



R

11

[k,v]

R

22

[k,v]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

34

[v]=M[v]NIntegrate[



R

11

[k,v]

R

22

[k,v]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

22

[v]=M[v]NIntegrate[

2

Abs[

R

22

[k,v]]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

23

[v]=M[v]NIntegrate[

2

Abs[

R

22

[k,v]]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

32

[v]=M[v]NIntegrate[

2

Abs[

R

22

[k,v]]

2

Abs[∅[k]]

,{k,0,100000}];

ρ

33

[v]=M[v]NIntegrate[

2

Abs[

R

22

[k,v]]

2

Abs[∅[k]]

,{k,0,100000}];ρ[v_]=

ρ 11 [v]	ρ 12 [v]	ρ 13 [v]	ρ 14 [v]
ρ 21 [v]	ρ 22 [v]	ρ 23 [v]	ρ 24 [v]
ρ 31 [v]	ρ 32 [v]	ρ 33 [v]	ρ 34 [v]
ρ 41 [v]	ρ 42 [v]	ρ 43 [v]	ρ 44 [v]

;A[v_]=Eigenvalues[ρ[v]]//FullSimplify;list=Range[0,14];n=Map[(#*

b

0

)&,list]//N;Do[Print[{A[v],v}],{v,n}]

NIntegrate

:Integral and error estimates are 0 on all integration subregions. Try increasing the value of the MinRecursion option. If value of integral may be 0, specify a finite value for the AccuracyGoal option.

NIntegrate

:Integral and error estimates are 0 on all integration subregions. Try increasing the value of the MinRecursion option. If value of integral may be 0, specify a finite value for the AccuracyGoal option.

NIntegrate

:Integral and error estimates are 0 on all integration subregions. Try increasing the value of the MinRecursion option. If value of integral may be 0, specify a finite value for the AccuracyGoal option.

General

:Further output of NIntegrate::izero will be suppressed during this calculation.

{{0.,0.,0.,0.},0.}

{{0.,0.,0.,0.},0.893244}

{{0.,0.,0.,0.},1.78649}

{{0.,0.,0.,0.},2.67973}

{{0.,0.,0.,0.},3.57298}

{{0.,0.,0.,0.},4.46622}

{{0.,0.,0.,0.},5.35946}

{{0.,0.,0.,0.},6.25271}

{{0.,0.,0.,0.},7.14595}

{{0.,0.,0.,0.},8.03919}

{{0.,0.,0.,0.},8.93244}

{{0.,0.,0.,0.},9.82568}

{{0.,0.,0.,0.},10.7189}

{{0.,0.,0.,0.},11.6122}

{{0.,0.,0.,0.},12.5054}

Out[]=

D0[Null]