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Green's Function

  • Thread starter Mancho
  • Start date
  • #1
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Homework Statement



I'm asked to calculate Green's function's real and imaginary parts.
The expression for the given Green's function is:

g00=[1-(1-4t2(z-E0)-2)1/2]/2t2(z-E0)-1 (1)
Where, z is the complex variable: z= E+iO+ (2)

Homework Equations



Complex number definition: Z = x + iy, where x is the real part and iy - imaginary.

The Attempt at a Solution


To separate real and imaginary parts I tried to express g00 in the form: g00= x+iy

First I simplified the (1) by multiplying the denominator and numerator by (z-E0).
The result is g00= 1/2t2[(z-E0)-(1-4t2)]1/2.

Then I'm stuck. I don't know how to remove the square root to divide real and imaginary parts. I'm not even sure if it is the pure math problem or if I have to take into consideration anything else.

I would appreciate any help.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Welcome to PF!

I'm asked to calculate Green's function's real and imaginary parts.

I don't know how to remove the square root to divide real and imaginary parts.
Hi Mancho! Welcome to PF! :smile:

Hint: the square-root of re is (√r)eiθ/2, and so its real and imaginary parts are (√r)cos(θ/2) and (√r)sin(θ/2) :wink:
 
  • #3
7
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Thanks a lot tiny-tim!

I guessed from your hint I had to use polar coordinates and it worked great! I got what I was supposed to. Maybe I will upload the solution later when I have time.

Thanks again! :)
 

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