I had another look at the problem. With the code below (copy of Marco's code above with slight modifications) everything seems to be ok. I have the idea that during the definitions of the functions Mathematica does some evaluations, and the result of these depend on whether numbers are already assigned or not. But this is just an assumption. Note that I use Setdelayed and plug in the parameters in T22 (and T22post) as variables of these functions. The code give the same results for T and Tpost even if you switch all the Clear-statements at the beginning on.

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

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

And here my code:

In[1]:= (*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[kn_, a_] := 
  Evaluate[(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) /. b -> a + d];

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

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

T22post[kn_, a_] := 
  Evaluate[(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) /. b -> a + d];


Tpost[kn_, a_] = 1/(T22post[kn, a]*(T22post[kn, a])\[Conjugate]);

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



Out[30]= True

Example

In[30]:= T[1, 1]
Tpost[1, 1]

Out[30]= 2.927595687384534*10^-822 + 0.*10^-850 I

Out[31]= 2.92759568738453*10^-822 + 0.*10^-850 I

In[32]:= T22[1, 1]
T22post[1, 1]

Out[32]= 5.844460807504422*10^410 - 3.400313161721839*10^397 I

Out[33]= 5.84446080750442*10^410 - 3.40031316172184*10^397 I

That is not the case on my system.

I inserted a statement to print T22 in both notebooks. They are quite different.

I suggest to define functions T22 and T with ALL parameters as arguments (I won't do it, it is late now). And I would define all functions with a SetDelayed

Attachments:

Ok, so what I understand is that, there is something odd happening, the function is definitely not the same depending on how I assign values to my parameters as Marco clearly demonstrated. Both Marco and Hans, you are advicing me to hold any evaluation until the plot. Did I get it right?

You are also suggesting this procedure would give the correct answer. In your opinion, can I really trust this is the case or should I use a different program just to be sure, like Matlab; or will I find the same issue there?

Thanks.

Ok, then I'll rest assured that delaying is the correct procedure, Hans. Thank you very much for your time. :)

The thing that intrigues me most is what exactly the definition

T[a_] = K + hv

has got to do with the plot - it is a function of one variable. There

ContourPlot[T[a,b], {a, 0.0,  1.0},  {b, 0.0,  1.0}]

T is a function of two variables. So the definition is inconsequential and should give an empty image, should it not? It therefore appears that T as a function of two variables must be defined somewhere else in the code/notebook. It would be useful to have that definition.

Cheers,

Marco

And what is hv?

I am a bit puzzled. You define T[a_] = ..... and you do a ContourPlot[ T[a, b].

Your definition of T is not a SetDelayed : T[a_] := expr and T[a,b] is nowhere defined. So the ContourPlot shouldN#t work at all.

Furthermore your function is linear in a and b. When I put things together I arrive at

Clear[TT]
TT[a_, b_] := U + V + h v (a + b) + h v

and this shouldn't give the ContourPlots you show us. Perhaps it is a good idea when you show a notebook with a bit more code.

And perhaps is your problem that T doesn't know the right parameters. Perhaps you should define

Clear[TT]
TT[a_, b_, U_, V_, h_, v_] := U + V + h v (a + b) + h v

but this is still linear in a and b

smile

I'll admit I hate the white spots, haha, but that's not the problem. The problem is that both contour plots that appear above come from the same function (and the same ContourPlot instructions). The order in which I assign values to my parameters alters the plot.