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!

2 questions

  1. Apr 23, 2009 #1
    1, apparently

    [itex]\frac{1}{2} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(-|\xi|) 4 \phi_{\xi \eta} d \xi d \eta=0[/itex]

    also apparently this is obvious after only doing the eta integral. any ideas why?

    2, what is [itex]\nabla^2 f(x)[/itex] where [itex]f(x)=-|x|^2[/itex]
    the answers say its -4
    when i just do the second derivative with respect to x i get -2
    and when i use index notation i get -6 since
    [itex]\partial_i \partial_i r_j r_j = \partial_i (2 \delta_{ij} r_j)=2 \partial_i r_i = 2 \delta_{ii} =6[/itex]

    what is going on here???
  2. jcsd
  3. Apr 23, 2009 #2


    User Avatar
    Science Advisor

    Latex still isn't working so I had to look at your LaTex code.

    For problem 1, what is "phixi, eta"?

    For the second, "nabla^2" is usually defined for functions of several variables. If f(x) really is |x|2= x2, then the second derivative is 2 as you say. If x is a two dimensional vector with x= <x, y>, then |x|= x2+ y2 and its Laplacian is 4. If x is a three dimensional vector with x= <x, y, z> then |x|= x2+ y2 and its Laplacian is 6. (More generally, if x is an n-dimensional vector, its Laplacian is 2n.)
  4. Apr 24, 2009 #3
    ok. thanks i follow the laplacian thing now.

    phi_xi,eta is the derivative of phi wrt xi and then wrt eta
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook