1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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! :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook