1. Not finding help here? Sign up for a free 30min 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!

Curvilinear Coordinates and Vector Calculus

  1. Nov 4, 2011 #1
    1. The problem statement, all variables and given/known data

    With [itex]\vec{L}[/itex] = -i[itex]\vec{r}[/itex] x [itex]\nabla[/itex], verify the operator identities

    [itex]\nabla = \hat{r}\frac{\partial }{\partial \vec{r}}-i\frac{\vec{r}\times\vec{L}}{r^{2}}[/itex]
    and
    [itex]\vec{r} \bigtriangledown ^2 - \bigtriangledown (1+\vec{r}\frac{\partial }{\partial \vec{r}})=i\bigtriangledown \times \vec{L}[/itex]


    2. Relevant equations



    3. The attempt at a solution

    ... I tried to expand it, and use some identities... But the equation becomes super complicated... Help!
     
  2. jcsd
  3. Nov 4, 2011 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    I don't see other way to do it other than expanding and writing the nabla operator in spherical coordinates...The only identity you need is the one for double vector product

    [tex] \vec{A}\times \left(\vec{B}\times\vec{C}\right) = \ ... [/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Curvilinear Coordinates and Vector Calculus
  1. Vector Calculus (Replies: 8)

Loading...