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How do you graph this function

Posted 10 years ago

I'm have trouble graphing this function [1/(8??)][(z/a0)^(3/2)][zr/a_0][e^(-zr/2a0)][sin(?)][e^(±i?)] can anyone help me graph this please

POSTED BY: zachary nichols
11 Replies

Oh okay thanks you

POSTED BY: zachary nichols

Hi,

What I have done here is, I have taken the real part of the wave function and plotted it.

From Euler's law,

Exp[\[Phi]]= Cos[\[Phi]]+ I Sin[\[Phi]]

and the real part is only Cos[Phi].The consideration of only the real part of the wave function is due to the fact that,

  1. You can not plot an imaginary function.

  2. The system is real. It is not imaginary. We assume a wave function to be imaginary because it is more understandable and it simplifies the calculation.

POSTED BY: suvadip mandal

may I ask how you got the cos[phi] form what it was of e^±i[phi]

suvadip mandal

Sincerely, Zachary

POSTED BY: zachary nichols

Hi Zachary,

I was checking your notebook that you have uploaded here and I have found some discrepancies in your notebook.

Are You trying to plot some wave functions for some conditions? (Like for n=2, l=1, m=0) Because I noticed that,

Your wave function is different in two places. In one case, there is a Sinh[\[Theta]] in another case, there is Sin[\[Theta]].

Also I don't think you can plot a wave function with imaginary quantities involved in it. Because I tried to plot the following,

Plot[Exp[I x],{x,0,10}]

and it gives me this,

enter image description here

Means nothing.

So perhaps you should take care of the real part and imaginary part separately.

Also my idea is, a wave function can be imaginary but to plot the wave function, you can take only the real part in consideration because the the system you are dealing with is real, not imaginary. In that case, the plot can be done.

And one more thing, I think I understand why did not you get any plot.

Your wave function is

1/(8 Sqrt[Pi]) (z r/a0)^(3/2) (z r/a0) Exp[-z r /(2 a0)] Sin[\[Theta]] Cos[\[Phi]]

where a0 = 5.29177*10^-11 and z, r are suitable parameters.Now as a0 is in denominator and it has a very small value, it shows me

"Infinite expression 1/0 encountered."

because in that case,Exp[z r/(2 a0)] goes to infinity, i.e. the wave function diverges and a wave function can not diverge.

I checked it with relatively large value if a0, (say 1) and I have got a plot.

Manipulate[SphericalPlot3D[1/(8 Sqrt[Pi]) (z r/a0)^(3/2) (z r/a0) Exp[-z r /(2 a0)] Sin[\[Theta]] Cos[\[Phi]], {\[Theta], 0,Pi}, {\[Phi], 0, 2 Pi}], {z, 1, 4, 1}, {r, 0.001, 1}]

This is the plot I have got for z=1, r=1.

enter image description here

Also, If you are trying to plot the probability density function in 3D,

Manipulate[SphericalPlot3D[(1/(8 Sqrt[Pi]) (z r/a0)^(3/2) (z r/a0) Exp[-z r /(2 a0)] Sin[\[Theta]] Cos[\[Phi]])^2, {\[Theta], 0,Pi}, {\[Phi], 0, 2 Pi}], {z, 1, 4, 1}, {r, 0.001, 1}]

This is the plot I have got for z=1, r=1.

enter image description here

Sincerely, Suvadip

Attachments:
POSTED BY: suvadip mandal

This is the notebook I've been working on

Attachments:
POSTED BY: zachary nichols

can anyone please help

POSTED BY: zachary nichols

when I tried to plot it i got:

Options expected (instead of {[Phi],0,2Pi}) beyond position 3 in the SphericalPlot3D. An option must be a rule or a list of rules.

(paraphrased do to inability to copy and paste)

POSTED BY: zachary nichols

1) Looks like you did not get parentheses matched when re-typing Isaac's example.

2) Could you save what you have in a notebook file (.nb) and attach that file to a post? (With the "Add a file to this post" button.)

Simple example attached.

Attachments:
POSTED BY: Bruce Miller

Hi, The syntax and arguments to the SphericalPlot3D seem to be incorrect (Please follow the link to the documentation).

Assuming I typed up the equation with the proper syntax by removing the extra [], I was unable to get a plot, so maybe the equation needs to be checked for correctness(?). It plots something for a0->1 (or values that aren't too small).

SphericalPlot3D[
 1/(8 (Sqrt[Pi])) ((1 (r))/(a0))^(3/
      2) ((1 (r))/(a0)) (E^(((-1) (r))/(2 (a0)))) (Sinh[
     Theta]) (E^( Phi)) /. {r -> 1, a0 -> 1}, {Theta, 0, 2 Pi}, {Phi, 
  0, 2 Pi}]
POSTED BY: Isaac Abraham

I typed this:

SphericalPlot3D [ 1/(8*(\[Sqrt](\[Pi])))*((1*(r))/(5.29177*10^(-11)))^(3/2)*((1*(r))/(5.29177*10^(-11)))*
    (E^(((-1)*(r))/(2*(5.29177*10^(-11)))))*(Sinh(\[Theta]))*(E^(\[ImaginaryI]*\[Phi])), 
   {r,0,2Pi},{\[Theta],0,2Pi},{\[Phi],0,2Pi}]

        z = 1

        a_0 (Bohr radius) = 5.29177*10^(-11)
POSTED BY: zachary nichols

When I copy and paste the code, I am getting like this,

[1/(8 \[Sqrt]\[Pi])][(z/a0)^(3/2)][zr/a_ 0][e^(-zr/2 a0)][sin (\[CapitalTheta])][e^(\[PlusMinus]i\[CapitalPhi])]

Now can you tell me what is the variable and what are the parameters?

Also what is a_0? Is it a constant? Anyway if you have typed in Mathematica exactly the same you have uploaded here,then I must say, you have typed the syntax in a wrong way. Like the built in Mathematica symbol for sin in 'Sin', for exponential function, it is 'Exp' or 'E' etc.

I think you should see the documentation properly.

sincerely,

Suvadip

POSTED BY: suvadip mandal
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