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Green's Function

  1. May 20, 2009 #1
    1. The problem statement, all variables and given/known data

    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)

    2. Relevant equations

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

    3. 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.
     
  2. jcsd
  3. May 20, 2009 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Welcome to PF!

    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:
     
  4. May 22, 2009 #3
    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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