Hello guys I am trying to make a 3d plot out of a 2d figure, but things are going sideways. My commands are
$Assumptions = Element[A | \[Epsilon] | m | Subscript[\[CapitalOmega],0] | \[Mu] | \
[Nu], Reals] && A > 0 && \[Epsilon] > 0 && 0 < \[Nu] < \[Pi] && m > 0 && Subscript[\
[CapitalOmega], 0] > 0 && \[Mu] > 0;
(Variables used)
Np = 10^5;
\[Epsilon] = 1.0 10^(-1);
m = 6.49*10^(-26);
Subscript[a, s] = 9*10^(-6);
A = 5*10^(-6);
\[HBar] = 1.054571817*10^(-34) ;
Subscript[\[CapitalOmega], 0] = 2 \[Pi] 200;
Subscript[g, 2 D] = Sqrt[((m Subscript[\[CapitalOmega], 0])/(2 \[Pi] \[HBar]))]*(4 \
[Pi] \[HBar]^(2) Subscript[a, s])/ m
\[Mu] = 9.0 10^(-11);
(Defining my function-Angular part)
Subscript[\[Xi], tf] = Sqrt[(\[Mu] - (\[HBar] \[Epsilon])/(2 m)
(Cos[\Nu]])^2)/Subscript[g, 2 D]]
(Ploting the angular part)
Plot[{Abs[Subscript[\[Xi], tf]^{2}]}, {\[Nu], 0, \[Pi]},
AxesStyle -> Arrowheads[{0.0, 0.03}],
LabelStyle -> Directive[Black, 28, Bold],
AxesLabel -> {Style[\[Nu], 28, Black],
Style[Abs[(Subscript[\[Xi], TF])^2], 28, Black]},
PlotLegends -> Style[Abs[Subscript[\[Xi], TF]^2], 28, Black],
PlotRange -> Automatic, PlotStyle -> {{Blue, Thick}},
ImageSize -> Large,
Ticks -> {{0, \[Pi]/4, \[Pi]/2, 3*\[Pi]/4, \[Pi]}, Automatic}]
(Now the full funciton with radial part)
\[Psi][r_, \[Nu]_] =
Abs[(((m Subscript[\[CapitalOmega], 0])/(\[Pi] \[HBar]))^(1/
4) Exp[-((m Subscript[\[CapitalOmega], 0] )/(
2 \[HBar]))*(r - A)^2] Subscript[\[Xi], tf])^2];
escalaTF = A + A/3;
(Density plot of full function)
DensityPlot[\[Psi][Sqrt[x^2 + (1 + \[Epsilon]) z^2],
ArcCos[(z *Sqrt[1 + \[Epsilon]])/
Sqrt[x^2 + (1 + \[Epsilon]) z^2]]], {x, -escalaTF,
escalaTF}, {z, -escalaTF, escalaTF}, Exclusions -> None,
PlotPoints -> 100, ColorFunction -> "BlueGreenYellow",
LabelStyle -> {23}, PlotLegends -> Automatic]
(UP UNTIL THIS POINT IM GETTING WHAT I NEED, NOW THE PROBLEM BEGINS)
(I want the full 3d vizualization of my sphere, so I try the commands)
\[Psi][x_, z_] = \[Psi][Sqrt[x^2 + (1 + \[Epsilon]) z^2],
ArcCos[(z *Sqrt[1 + \[Epsilon]])/Sqrt[x^2 + (1 + \[Epsilon]) z^2]]]\[Psi][x_, z_] = \
[Psi][Sqrt[x^2 + (1 + \[Epsilon]) z^2],
ArcCos[(z *Sqrt[1 + \[Epsilon]])/Sqrt[x^2 + (1 + \[Epsilon]) z^2]]]
Raio = A^(2);
a[x_, z_] =
Piecewise[{{\[Psi][x, Sqrt[(Raio - x^2)/(1 + \[Epsilon])]],
x^2 + (1 + \[Epsilon]) z^2 < Raio}, {0,
x^2 + (1 + \[Epsilon]) z^2 > Raio}}]
DensityPlot[
a[x, z], {x, -escalaTF, escalaTF}, {z, -escalaTF, escalaTF},
Exclusions -> None, ColorFunction -> "BlueGreenYellow",
PlotRange -> Automatic, PlotPoints -> 100, LabelStyle -> {23},
PlotLegends -> Automatic]
So the idea is that in spherical coordinates the nu angle goes from 0 to pi in the z direction, and the phi angle gos from 0 to 2 pi in the x-y plane. I want to plot the full sphere seen from the ourside so i try to rotate the figure of the shell on the phi angle from 0 to 2 pi.
I hope you can note this is not the full sphere seen from the outside. It should have only a small blue circle on the south and north poles, and a yellow horizontal band at the equator and not a blue vertical band. I don't understand what I did wrong. This is not the usual spherical coordinates, since I added a distortion on the z direction to make an ellipsoid if wanted.
I also tried a 3d plot
Subscript[\[Psi], S][
r_, \[Nu]_] = ((
m Subscript[\[CapitalOmega], 0])/(\[Pi] \[HBar]))^(1/4) Exp[-((
m Subscript[\[CapitalOmega], 0] )/(
2 \[HBar]))*(r - A)^2] Subscript[\[Xi], tf];
Subscript[\[Psi], S][x_, y_, z_] =
Subscript[\[Psi], S][Sqrt[x^2 + y^2 + (1 + \[Epsilon]) z^2],
ArcCos[(z *Sqrt[1 + \[Epsilon]])/
Sqrt[x^2 + y^2 + (1 + \[Epsilon]) z^2]]]
Raio = A^(2);
a[x_, y_, z_] =
Piecewise[{{Subscript[\[Psi], S][x,
Sqrt[(Raio - x^2 - y^2)/(1 + \[Epsilon])]],
x^2 + y^2 + (1 + \[Epsilon]) z^2 < Raio}, {0,
x^2 + y^2 + (1 + \[Epsilon]) z^2 > Raio}}]
DensityPlot3D[
a[x, y, z], {x, -escalaTF, escalaTF}, {y, -escalaTF,
escalaTF}, {z, -escalaTF, escalaTF},
ColorFunction -> "BlueGreenYellow", PlotRange -> Automatic,
PlotPoints -> 50, LabelStyle -> {23}, PlotLegends -> Automatic]
But this has the same problem of the blue band going from north to south as in the other figure.