0
|
8327 Views
|
3 Replies
|
1 Total Likes
View groups...
Share
GROUPS:

# How find the exact intersections in the graphs of wave equations

Posted 10 years ago
 (1/(Sqrt[Pi])(1/a0)^(3/2)Exp[-r /(a0)]) (1/(8Sqrt[Pi])(1/a0)^(3/2)(2-(r/a0))Exp[-r /(2 a0)]) (81/(Sqrt[3Pi])(1/a0)^(3/2)(27-(18r/a0)+2(r^(2)/a0^2))  These are three wave equations that I need to find where they intersect all at the same point. However every time I set them equal they say one is protected. I don't know what I need to do to allow me to do what I need done Can someone help. Sincerely, Zachary Nichols
3 Replies
Sort By:
Posted 10 years ago
 Zachary, It will be helpful if you cut and paste the code you are using in a code box (see the <> icon at top left) and indicate whether r is two- or three-dimensional, etc. WCC
Posted 10 years ago
 Set a0 = 1 and define 3 functions. These are evidently the 1 s, 2 s and 3 s wavefunctions of the hydrogen atom.With corrections : f1[r_] := (1/(Sqrt[Pi]) Exp[-r]) f2[r_] := (1/4 Sqrt[2 Pi]) (2 - r) Exp[-r/2 ] f3[r_] := (1/(81 Sqrt[3 Pi])) (27 - 18 r + 2 r^2) Exp[-r/3 ] Plot[{f1[r], f2[r], f3[r]}, {r, 0, 10}] The plot will show that there are no triple intersections (except at r = Infinity).
Posted 10 years ago
 Thank you S M Blinder; however now I'm working with three dimensional functions and trying to find the the exact intersections how would I do that This is the graph of the wave equations i want to find the intersections of Manipulate[SphericalPlot3D[{(1/(8Sqrt[Pi])(1/a0)^(3/2)(r/a0)Exp[-r /(2 a0)]Sin[[Theta]]Cos[[Phi]])^2,(1/(Sqrt[81Pi])(1/a0)^(3/2)(6-(r/a0))(r/a0)Exp[-r /(3a0)]Sin[[Theta]]Cos[[Phi]])^2,(1/(4Sqrt[2Pi])(1/a0)^(3/2)(r/a0)Exp[-r /(2 a0)]Cos[[Theta]])^2},{[Theta],0,2Pi},{[Phi],0,2Pi}],{r,0.001,1}]a0=1Sincerely, Zachary Nichols