Complex Conjugate of a Function

[Thomas Markovich]

Ok,

So heres what I have found that works. The complex conjugate of e^ix  
is the same as taking the complex conjugate of the answer from that  
function. So, what I need to do is generate a vector from the function  
b(x) which is defined as:

((-.0017813.*exp(-4*i*x) + -.022768.*exp(-3*i*x) + -. 
060292.*exp(-2*i*x) + -.59101.*exp(-x) + .54138.*exp(0) + -. 
59101.*exp(x) + -.060292.*exp(2*i*x) + -.022768.*exp(3*i*x) + -. 
0017813.*exp(4*i*x)) + (.0031691.*exp(-4*i*x) + .030436.*exp(-3*i*x)  
+ .12741.*(exp(-2*i*x)) + .69486.*exp(-x*i) + 0.*exp(0) + -. 
69486.*exp(x*i) + -.12741.*exp(2*i*x) + -.030436.*exp(3*i*x) + -. 
0031691.*exp(4*i*x)))/(2*sqrt(pi))

and I have found that conj(some vector) ends up being defined. I have  
also discovered that I can just do, assuming that k is my vector  
generated from b(x):

  conj(k) .* diff(k) - k .* diff(conj(k))

And this should give me the probability current. Anyways, what I am  
struggling with now is, how do I define b(x) with x being [-2*pi: . 
01 : 2*pi] (-2*pi < x < 2*pi) to get into a vector k. What I have now  
is k = [b(x)]; but have tried everything I can think of.

Anyways, thank you for your help thus far. Also, if there is anything  
in my thought process thus far that is ludricous or just doesn't make  
sense; please don't hesitate to correct me.

Regards,

Thomas Markovich
Undergraduate Research Assistant
University of Houston

On Oct 8, 2008, at 3:24 PM, Thomas Markovich wrote:

> Hi,
>
> I am using octave and I am trying to find the probability current of  
> of a set of wave functions. To do this though, I get
>
> (¥*) d/dx(¥) - ¥(d/dx(¥*))
>
> I have tried to use both functions, conj and ' to find the conjugate  
> but octave gives me the following error.
>
> octave-3.0.2:59> conj(b(x))
> ans =
>
> Columns 1 through 6:
>
>   0.792789 - 0.000000i   0.521003 - 0.044985i   0.361599 -  
> 0.061587i   0.263736 - 0.026430i   0.163356 + 0.047835i   0.013050 +  
> 0.086010i
>
> Columns 7 through 12:
>
>  -0.173588 + 0.028121i  -0.377793 - 0.064103i  -0.673954 -  
> 0.079818i  -1.212822 - 0.014479i  -2.150759 + 0.048640i  -3.688296 +  
> 0.059676i
>
> Column 13:
>
>  -6.190114 + 0.027294i
>
> error: conj: argument undefined
>
> Any help would would be much appreciated.
>
> Thomas Markovich
> Undergraduate Research Assistant
> University of Houston