(*conical intersection; solution of the 2x2 case*)
E1=Sqrt[0.1*x^2+0.1*y^2]
E2=-Sqrt[0.1*x^2+0.1*y^2]
E1=Sqrt[0.1*x^2+0.1*y^2]
E2=-Sqrt[0.1*x^2+0.1*y^2]
Plot[{Sqrt[0.1]x,-Sqrt[0.1]x},{x,-1,1},PlotStyle->{Directive[Darker[Darker[Green]], Thickness[0.015]],Directive[Orange, Thickness[0.015]]},AxesLabel->{(Subscript[ξ, 1]),E}, Epilog->{Inset[Style["E+",40,FontWeight->"Bold"],{0.5,Center},{0.5,Bottom}],Inset[Style["E-",40,FontWeight->"Bold"],{0.5,Bottom},{0.5,Bottom}]}]
Show[
Plot3D[0.,{x,-15,15},{y,-11,11},Axes->False,PlotStyle->Directive[Opacity[0.30],RGBColor[0.,1.,0]]],
Plot3D[E2,{x,-15,0},{y,-11,11},PlotStyle->Directive[Opacity[0.80],Darker[Darker[RGBColor[0,1.,0]]]]],
Plot3D[E2,{x,0,15},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1,{x,-15,0},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1,{x,0,15},{y,-11,11},PlotStyle->Directive[Opacity[0.80],Darker[Darker[RGBColor[0.,1.,0]]]]],
Graphics3D[{Red,Thickness[0.006],Line[{{0,0,0},{8,0,0}}]}],
Graphics3D[{Red,Thickness[0.003],Line[{{8.2,0,0},{7.5,0.,0.05}}]}],
Graphics3D[{Red,Thickness[0.003],Line[{{8.2,0,0},{7.5,0.,-0.05}}]}],
Graphics3D[{Red,Thickness[0.006],Line[{{0,0,0},{4,8,0}}]}],
Graphics3D[{Red,Thickness[0.003],Line[{{4.0,8.1,0},{3.5,8.,0.05}}]}],
Graphics3D[{Red,Thickness[0.003],Line[{{4.0,8.1,0},{3.5,7.5,-0.05}}]}]
]
Show[
Plot3D[0.,{x,-15,15},{y,-11,11},RegionFunction->Function[{x,y,z},z≤-1],Axes->False,PlotStyle->Directive[Opacity[0.30],RGBColor[0.,1.,0],AxesLabel->{"x","y","Energy"}]],
Plot3D[E2,{x,-15,0},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[0,1.,0]]],
Plot3D[E2,{x,0,15},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1,{x,-15,0},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1,{x,0,15},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[0.,1.,0]]],
ParametricPlot3D[{x,0,parab}, {x,-15,15},PlotStyle->{Red,Thickness[0.008]}]
]
parab=0.005x^2
E1p=Sqrt[0.4*(x-8)^2+0.4*y^2]+0.32
E2p=-Sqrt[0.4*(x-8)^2+0.4*y^2]+0.32
E1l=Sqrt[0.025*(x+8)^2+0.025*y^2]+0.32
E2l=-Sqrt[0.025*(x+8)^2+0.025*y^2]+0.32
Show[
Plot3D[0.,{x,-15,15},{y,-11,11},RegionFunction->Function[{x,y,z},z≤-1],Axes->False,PlotStyle->Directive[Opacity[0.30],RGBColor[0.,1.,0],AxesLabel->{"x","y","Energy"}]],
Plot3D[E2,{x,-15,0},{y,-11,11},PlotStyle->Directive[Opacity[0.80],Darker[Darker[RGBColor[0,1.,0]]]]],
Plot3D[E2,{x,0,15},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1,{x,-15,0},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1,{x,0,15},{y,-11,11},PlotStyle->Directive[Opacity[0.80],Darker[Darker[RGBColor[0.,1.,0]]]]],
Plot3D[E2p,{x,-15,8},{y,-11,11},RegionFunction->Function[{x,y,z},Abs[z]≤0.5],PlotStyle->Directive[Opacity[0.80],Darker[Darker[RGBColor[0,1.,0.]]]]],
Plot3D[E2p,{x,8,15},{y,-11,11},RegionFunction->Function[{x,y,z},Abs[z]≤0.5],PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1p,{x,-15,8},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[1.,1.,0]]],
Plot3D[E1p,{x,8,15},{y,-11,11},PlotStyle->Directive[Opacity[0.80],Darker[Darker[RGBColor[0,1.,0.]]]]],
Plot3D[E2l,{x,-15,-8},{y,-11,11},RegionFunction->Function[{x,y,z},Abs[z]≤0.4],PlotStyle->Directive[Opacity[0.80],Darker[Darker[RGBColor[0,1.,0]]]]],
Plot3D[E2l,{x,-8,15},{y,-11,11},RegionFunction->Function[{x,y,z},Abs[z]≤0.4],PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1l,{x,-15,-8},{y,-11,11},PlotStyle->Directive[Opacity[0.80],RGBColor[1,1.,0]]],
Plot3D[E1l,{x,-8,15},{y,-11,11},PlotStyle->Directive[Opacity[0.80],Darker[Darker[RGBColor[0.,1.,0]]]]],
ParametricPlot3D[{x,0,parab}, {x,-15,15},PlotStyle->{Red,Thickness[0.008]}]
]