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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
____________________________________________________________________


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