- #1
elduderino
- 57
- 0
I have an expression which has six terms. I am posting one of the terms, in its basic form:
[tex]
f1= \int \frac{d\vec{k}}{( \xi [\vec{k}] + i d - \xi [\vec{k}-\vec{b}] ) ( \xi [\vec{k}] + i c + i d - \xi [\vec{k}-\vec{a} - \vec{b}]) }
[/tex]
Then there are f2, f3,f4..f6. They are all complex conjugates.
The six terms together constitute the expression [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex]. I am to integrate and hence evaluate and visualize the function [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex] in Mathematica. I was able to do the one-dimensional case correctly, where all the variables can be treated as scalars. However I am having trouble doing the 2-D case.
In fact, I am a little unsure about how the math works when vectors are involved, and also how to make mathematica evaluate this integration for me. Here is what I tried.
I declared
k={kx,ky} ... a={ax,ay} ... etc
The function [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex] now becomes a list as:
[tex] F(\vec{a},\vec{b},c,d,\vec{k}) = \{ F(ax,bx,c,d,kx) , F(ay,by,c,d,ky) \} [/tex]
Now if I use: Integrate[F, k]
I should expect an output of the form {Expr1,Expr2}
However, I get an error... "Integrate::ilim: Invalid integration variable or limit(s) in {kx,ky}."
Can somebody explain what I am doing wrong here?
Even more fundamentally, I somehow doubt if this approach to carrying out the integration is correct. Can someone hint how such integrations involving vector variables and complexes (iotas) are solved?
[tex]
f1= \int \frac{d\vec{k}}{( \xi [\vec{k}] + i d - \xi [\vec{k}-\vec{b}] ) ( \xi [\vec{k}] + i c + i d - \xi [\vec{k}-\vec{a} - \vec{b}]) }
[/tex]
Then there are f2, f3,f4..f6. They are all complex conjugates.
The six terms together constitute the expression [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex]. I am to integrate and hence evaluate and visualize the function [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex] in Mathematica. I was able to do the one-dimensional case correctly, where all the variables can be treated as scalars. However I am having trouble doing the 2-D case.
In fact, I am a little unsure about how the math works when vectors are involved, and also how to make mathematica evaluate this integration for me. Here is what I tried.
I declared
k={kx,ky} ... a={ax,ay} ... etc
The function [tex] F(\vec{a},\vec{b},c,d,\vec{k})[/tex] now becomes a list as:
[tex] F(\vec{a},\vec{b},c,d,\vec{k}) = \{ F(ax,bx,c,d,kx) , F(ay,by,c,d,ky) \} [/tex]
Now if I use: Integrate[F, k]
I should expect an output of the form {Expr1,Expr2}
However, I get an error... "Integrate::ilim: Invalid integration variable or limit(s) in {kx,ky}."
Can somebody explain what I am doing wrong here?
Even more fundamentally, I somehow doubt if this approach to carrying out the integration is correct. Can someone hint how such integrations involving vector variables and complexes (iotas) are solved?