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!

Nabla Operator

  1. Jan 10, 2005 #1

    Dear Friends,

    Another question for dummies...

    The operator "nabla" can be locates before or after a vector or a tensor. If you take the vector A, "nabla A" is not the same that "A nabla" but, is it possible to obtain "nabla A - A nabla"? ¿And "(A nabla) A - A (nabla A)"?

  2. jcsd
  3. Jan 10, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    I hope u're not insinuating that we (me included) would be "dummies"... :mad:

    [tex] \nabla=\sum_{i=1}^{3} \frac{\partial}{\partial x_{i}} \vec{e}_{i} [/tex](1)
    in the cartezian system of coordinates
    [tex] \vec{A}\cdot \nabla=\sum_{i=1}^{3} A_{i}\frac{\partial}{\partial x_{i}} [/tex] (2)

    [tex] \nabla\cdot\vec{A}=\sum_{i=1}^{3} \frac{\partial A_{i}}{\partial x_{i}} [/tex] (3)

    That's all u need to know.
    [tex] [\nabla,\vec{A}]_{-}=:\nabla\cdot\vec{A}-\vec{A}\cdot \nabla [/tex]
    is kinda weird operator which is made from a multiplicative part and a differential part.
    I've never seen it in physics in this form.A bit different form can be found in QM with the operators of position and momentum in the coordinate representations.It's basicaly minus the fundamental commutator relations.

    Last edited: Jan 10, 2005
  4. Jan 10, 2005 #3

    No... the "dummie" in mathmatics and physics am I.
  5. Jan 10, 2005 #4


    User Avatar
    Science Advisor
    Homework Helper

    On a second thought about that commutator of operators,in analogy with the QM case,consider it to be applying on a scarar function [itex] \phi(\vec{r}) [/tex]

    [tex][\nabla,\vec{A}(\vec{r})]_{-}\phi(\vec{r})=:\nabla\cdot [\vec{A}(\vec{r})\phi(\vec{r})]-\vec{A}\cdot \nabla\phi(\vec{r})=[\nabla\cdot \vec{A}(\vec{r})] \phi(\vec{r}) [/tex]

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Nabla Operator
  1. Nabla operator (Replies: 8)

  2. Vector operations (Replies: 7)

  3. Operational amplifier (Replies: 2)

  4. Operational amplifier (Replies: 13)