l=1 H-Atom Wave Functions:
(* GRAPHICS--Hydrogen Atom Wave-Functions *)
Needs["Graphics`ParametricPlot3D`"]
(* Second, for [l=1, n=2,3], ie.,2p & 3p Orbitals *)
(* the Angular Part Squared for n=2,l=1,m=0 ie., 2pz *)
SphericalPlot3D[Evaluate[(Cos[th])^2],{th,0,Pi},
{ph,0,2Pi}]
-Graphics3D-
(* the (x,y=0,z)-Section of the Wave-Function Squared
for n=2,l=1,m=0 *)
Plot3D[(Sqrt[x^2+z^2]Exp[-Sqrt[x^2+z^2]/2]
(z/Sqrt[x^2+z^2]))^2,{x,-4,4},{z,-4,4},
PlotRange->{0,1}]
-SurfaceGraphics-
Show[%,ViewPoint->{0,-1,2}]
-SurfaceGraphics-
(* the Angular Part Squared for n=2,l=1,m=1, ie., 2px *)
SphericalPlot3D[Evaluate[(Sin[th]Cos[ph])^2],{th,0,Pi},
{ph,0,2Pi}]
-Graphics3D-
(* the (x,y,z=0)-Section of the Wave-Function Squared
for n=2,l=1,m=1 ie.,2px *)
Plot3D[(Sqrt[x^2+y^2]Exp[-Sqrt[x^2+y^2]/2]
(x/Sqrt[x^2+y^2]))^2,{x,-20,20},{y,-20,20},
PlotRange->{0,0.2}]
-SurfaceGraphics-
(* the (x,y,z=0)-Section of the Wave-Function Squared
for n=3,l=1,m=1 ie., 3px *)
Plot3D[((6Sqrt[x^2+y^2]-(x^2+y^2))Exp[-Sqrt[x^2+y^2]/3]
(x/Sqrt[x^2+y^2]))^2,{x,-20,20},{y,-20,20},
PlotRange->{0,5}]
-SurfaceGraphics-
(* Angular Part Squared for n=2,l=1,m=-1 ie., 2py *)
SphericalPlot3D[Evaluate[(Sin[th]Sin[ph])^2],{th,0,Pi},
{ph,0,2Pi}]
-Graphics3D-
(* the (x,y,z=0)-Section of the Wave-Function Squared
for n=2,l=1,m=-1 ie., 2py *)
Plot3D[(Sqrt[x^2+y^2]Exp[-Sqrt[x^2+y^2]/2]
(y/Sqrt[x^2+y^2]))^2,{x,-5,5},{y,-5,5},
PlotRange->{0,1}]
-SurfaceGraphics-
(* the (x,y,z=0)-Section of the Wave-Function Squared
for n=3,l=1,m=-1 ie., 3py *)
Plot3D[((6Sqrt[x^2+y^2]-(x^2+y^2))Exp[-Sqrt[x^2+y^2]/3]
(y/Sqrt[x^2+y^2]))^2,{x,-20,20},{y,-20,20},
PlotRange->{0,5}]
-SurfaceGraphics-
(* Radial Part Squared for n=2,l=1,m=-1 ie.,
for 2py along (x=0,y,z=0)-line *)
Plot[(y*Exp[-y/2])^2,{y,0,20},PlotRange->{0,1}]
-Graphics-
(* Radial Part Squared for n=3,l=1,m=-1 ie.,
for 3py along (x=0,y,z=0)-line *)
Plot[((6y-y^2)*Exp[-y/3])^2,{y,0,20},PlotRange->{0,20}]
-Graphics-
(* y^2 Weighted Radial Part for 3py
along (x=0,y,z=0)-line *)
Plot[(y^2)*((6y-y^2)*Exp[-y/3])^2,{y,0,20},
PlotRange->{0,500}]
-Graphics-
L=1 Wave Functions.JKB
This ends part 1 of the L=1 H-Atom Wave Functions Mathematica files.
You can now go on to the second and final
part, l = 1 H-Atom Wave Functions Contour Plots in 3-D, or return
to the notes.