Results 1 to 3 of 3

Math Help - Path integral

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    38

    Path integral

    I need to show that \int_{0,0}^{1,1}z^*dz is path dependent by choosing 2 paths. C_1 passes through (1,0) and C_2 passes through(0,1)

    Here's my attempt:

    path 1:
    \int_{0,0}^{1,1}z^*dz=\int_{0,0}^{1,1}(x-iy)(dx+idy)=\int_{0,0}^{1,1}(xdx+ydy)+i\int_{0,0}^  {1,1}(xdy-ydx)
    =\int_{0,0}^{1,0}(xdx+ydy)+\int_{1,0}^{1,1}(xdx+yd  y)+i\int_{0,0}^{1,0}(xdy-ydx)+i\int_{1,0}^{1,1}(xdy-ydx)
    =\left (\frac{x^2}{2}+\frac{y^2}{2}  \right )^{0,1}_{0,0}+\left (\frac{x^2}{2}+\frac{y^2}{2}  \right )^{1,1}_{0,1}+i\left (xy-yx  \right )^{0,1}_{0,0}+i\left (xy-yx  \right )^{1,1}_{0,1}
    =\frac{1}{2}-0+1-\frac{1}{2}
    the imaginary part cancels since xy-yx=0
    =1

    Following the same procedure for path 2:
    \int_{0,0}^{1,1}z^*dz=\int_{0,0}^{1,1}(x-iy)(dx+idy)=\int_{0,0}^{1,1}(xdx+ydy)+i\int_{0,0}^  {1,1}(xdy-ydx)
    =\int_{0,0}^{0,1}(xdx+ydy)+\int_{0,1}^{1,1}(xdx+yd  y)+i\int_{0,0}^{0,1}(xdy-ydx)+i\int_{0,1}^{1,1}(xdy-ydx)
    =\left (\frac{x^2}{2}+\frac{y^2}{2} \right )^{0,1}_{0,0}+\left (\frac{x^2}{2}+\frac{y^2}{2} \right )^{1,1}_{0,1}+i\left (xy-yx \right )^{0,1}_{0,0}+i\left (xy-yx \right )^{1,1}_{0,1}
    =\frac{1}{2}-0+1-\frac{1}{2}
    the imaginary part cancels since xy-yx=0
    =1

    I recover the same answer, what am I doing wrong?
    Last edited by synclastica_86; September 10th 2009 at 06:25 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    z=x+iy
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2009
    Posts
    38
    Yes but z^*=x-iy right?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Path Integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 26th 2010, 11:04 PM
  2. Path integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 8th 2010, 02:34 PM
  3. complex path integral
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: October 13th 2009, 12:09 PM
  4. Path Integral
    Posted in the Calculus Forum
    Replies: 7
    Last Post: December 11th 2008, 04:45 PM
  5. some help in Path integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 31st 2006, 11:38 PM

Search Tags


/mathhelpforum @mathhelpforum