Dear Hans,

@Marco: Which is the reason you don't use T22post in

Tpost[kn, a] = 1/(T22*(T22)[Conjugate]);

It is difficult to come up with a credible excuse for my stupid mistake. Sorry!

Best wishes,

Marco

The notebook ContourPlot 2.nb

gives the same as the first if you comment out the first three lines (the Clear commands) after second evaluation.

ClearAll doesn't appear to do anything anyway.

I think.

Cheers, Marco

If I run

(*ClearAll["Global`*"]*)
(*ClearAll["Global`*"]
ClearAll[Evaluate[$Context<>"*"]]*)

ClearAll["Global`*"];
energy = 0.027*eV;

eV = 1/27.2113845;
nm = 1/0.052917721092;

a0 = 4.65;
n = 0;
M = 4;
W = a0*(3*M + 1);

e = 1;
h = 1;
v = 0.003*137.036;

kmodC = (energy - e*VC)/(h*v);
kmodRG = (energy - e*VRG)/(h*v);
kmodRB = (energy - e*VRB)/(h*v);

kC = (kmodC^2 - kn^2)^0.5;
kRG = (kmodRG^2 - kn^2)^0.5;
kRB = (kmodRB^2 - kn^2)^0.5;

zC = (kn + I*kC)/((kn^2 + kC^2)^0.5);
zRG = (kn + I*kRG)/((kn^2 + kRG^2)^0.5);
zRB = (kn + I*kRB)/((kn^2 + kRB^2)^0.5);


T22 = ( E^(-2 I a (kC + kRG) + 
      I b (2 kRG + kRB)) ((zC zRG - 1)^2 E^(
        4 I (a - b) kRG) (-1 + zRB zRG)^2 + 
       2 E^(2 I (a - b) kRG)  (-zC (1 + zRG^2) + zRG + 
          zC^2 zRG)))/((-1 + zRG^2)^2);

T[kn_, a_] = 1/(T22*(T22)\[Conjugate]);

(*Parameters*)
VRG = 0.100*eV;
VRB = 0.001*eV;
VC = 0.001*eV;
b = (a + d);
d = 50*nm;
(*Parameters*)

T22post = ( 
    E^(-2 I a (kC + kRG) + 
      I b (2 kRG + kRB)) ((zC zRG - 1)^2 E^(
        4 I (a - b) kRG) (-1 + zRB zRG)^2 + 
       2 E^(2 I (a - b) kRG)  (-zC (1 + zRG^2) + zRG + 
          zC^2 zRG)))/((-1 + zRG^2)^2);

Tpost[kn_, a_] = 1/(T22*(T22)\[Conjugate]);

Evaluate[T[kn*(1/nm), (a/2)*nm] === Tpost[kn*(1/nm), (a/2)*nm]]

It turns out that the T and Tpost are not identical as Hans says. The first bits of the functions are a bit different:

T

Post

at the very end the "a" has a different factor.

In principle it is now easy to see what is happening. Just compare

TreeForm[Tpost[kn*(1/nm), (a/2)*nm]]

to

TreeForm[T[kn*(1/nm), (a/2)*nm]]

I agree that the delayed definition would probably be more appropriate.

Best wishes,

Marco

I think the problem is solved. It seems that there were problems with handing the parameters to the function(s). Look at my code ( a modificaton of Marco's code). It gives the same functions regardless where you do the assignments. And in my opinion Mathematica will do the job.

Yes, both Hans and Marco are totally right. I made a mistake in the example. I apologise for the confusion. I uploaded a 2 working notebooks, however, so it becomes more clear. I also edited that mistake now. Thanks again,

Edit: The notebooks contain a plot of what should be the same function. They vary only on the place where I assign the values of my parameters.

Planck's constant and escape velocity but I'll edit that to make it clearer, thanks for the reply :)

This time I was first (even though my post appears below)!

;-)

Marco

Simplify[T[a_]] does not simplify the definition of T. For that you must insert Simplify into the definition: T[a_]=Simplify[k+hv].

I think you'd get more and better responses if you supplied a complete working example. And admittedly I can be a bit dense as I'm not at all certain what the issue is that you're having trouble with.

I still don't understand what the issue is but a wild guess is that you don't like the fact that parts of one of the contour plots is "white". Usually to fix that one can use PlotRange -> All.