Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Does dP_x dP_y = d^2\vec P : Integration scalar / vector var

  1. Apr 14, 2017 #1
    Excuse me if this is a bad question but:



    Does ##d P_x d P_y = d^2 \vec P ##?



    I thought not because ##P_x ## is a scalar , a component of the vector, whereas ##\vec P ## is a vector?



    Thanks in advance
     
  2. jcsd
  3. Apr 15, 2017 #2

    haushofer

    User Avatar
    Science Advisor

    I'd say they're equal, but this is merely notation, no?
     
  4. Apr 15, 2017 #3
    mm I'm confused:

    Say I have ##\int dP_x dP_y e^{-\vec{P}^2}##

    if ##dP_x dP_y =d\vec P ##* then this is ## \int d\vec{P}e^{-\vec{P}^2}=\sqrt{\pi}##

    Since ##\vec P^2## is a scalar I can do the integral working with the components ##dP_x## and ##dP_y## however had it not been and just been ##\vec{P}## I don't know how you convert the integral between ##dP_x dP_y## and ##d\vec P ##

    So ##\int dP_x dP_y e^{-\vec{P}^2}=\int dP_x dP_y e^{-P_x^2-P_y^2}=\int dP_x e^{-P_x^2}\int dP_x e^{-P_y^2}=\sqrt{\pi}\sqrt{\pi}=\pi##

    so using * these don't agree?
     
  5. Apr 18, 2017 #4
    anyone? What have I done wrong here?
    Many thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Does dP_x dP_y = d^2\vec P : Integration scalar / vector var
  1. Vectors and Scalars (Replies: 3)

Loading...