Re: Plot Complex Interpol .Func.
- To: mathgroup at smc.vnet.net
- Subject: [mg9615] Re: Plot Complex Interpol .Func.
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Fri, 14 Nov 1997 21:39:56 -0500
- Organization: University of Western Australia
- Sender: owner-wri-mathgroup at wolfram.com
Debbie Leddon wrote:
> I am trying to solve the schrodinger equation as follows and I want to
> be able to plot the resulting interpolating function (which should
> contain complex values).
>
> In[6]:=Schrodinger[V_,A_] := D[f[a],{a,2}] + (V - A)f[a]]
>
> In[7]:= R[x_,y_] := x + I y
>
> In[8]:= V[R_,a_] :=
> R[1,2](-1/(Cos[a] - Sin[a]) -1/Sin[a] + 1/Cos[a])
>
> In[9]:= eq1 = 0 == Schrodinger[V[R,a],-900]
>
> Out[9]= 0==f[a] (900 + (1 + 2 I) (-Csc[a] + Sec[a] -
> 1/(Cos[a] - Sin[a])) + f''[a]
>
> In[10]:= soln =NDSolve[{eq1, f[0.00005] ==0, f'[0.00005] ==.5},
> f, {a, 0.00005, 0.785348}][[1]]
>
> Out[10]= {f->InterpolatingFunction[{{0.00005,0.785348}},"<>"]}
As you note above f is Complex.
> In[11]:= ParametricPlot[f /. soln[[1]], {a, 0.00005, 1}]
>
> The error message I got at this point was:
> function f/. soln[[1]] cannot be compiled; plotting will proceed.. f/.
> soln[[1]] does not evaluate to a real pair of numbers
> at a =0.000050041664...., etc.
>
> What went wrong ? How can I plot the interpolating function?
You need to plot the Re or Im parts. Also f is a function of the
parameter a. Finally, you can just use Plot; Evaluate improves the
efficiency:
Plot[Evaluate[Re[f[a] /. soln]], {a, 0.00005, 1}]
Plot[Evaluate[Im[f[a] /. soln]], {a, 0.00005, 1}]
Since you are interested in Quantum-based applications you might want to
have a look at the University of Western Australia library site where
there is a listing of our Physics Electronic Course Materials:
http://www.library.uwa.edu.au/edocs/ecourse/ecourse-phys.html
Second Year : Electromagnetism
Second Year : Quantum Mechanics
Third Year: Computational Physics
Third Year: Computational Biophysics
Of these, I am responsible for the 3rd year computational physics
course:
http://www.pd.uwa.edu.au/Physics/Courses/Third_Year/Computational_Physics.html
(which includes one Notebook devoted to the Schroedinger Equation) and
the second year Electromagnetism course:
http://www.pd.uwa.edu.au/Physics/Courses/Second_Year/ElectroMagnetism.html
You might also find the second year courseware at
http://www.pd.uwa.edu.au/Physics/Courses/Second_Year/Quantum.html
interesting.
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
____________________________________________________________________