How Can I Fix My Indicial Notation Practice?

[muzialis]

Hi there,

I am trying to get some practice with indicial notation.
I am failing as follows, to start with.
Given a vectorial function $$v_j = a_j e^{i(k_k x_k - \omega t)}$$ of spatial variables $$x_i$$ and time, given a tensor $$K_{ijkl}$$ I want to compute the quantity
$$K_{2jkl} v_{k,l}$$.
I get $$K_{2jkl} a_l i k_k e^{i(k_m x_m - \omega t)}$$, while the correct result is
$$K_{2jkl} k_k a_ l e^{i(k_m x_m - \omega t)}$$.

Can anybody help?

Thanks

 

[Fredrik]

I get a third result,
$$K_{2jkl}v_{k,l}=K_{2jkl}\partial_l\left(a_k e^{i(k_m x_m-\omega t)}\right) =K_{2jkl}ik_la_k e^{i(k_m x_m-\omega t)} =iK_{2jkl}v_k k_l.$$

Link to the LaTeX guide: https://www.physicsforums.com/showpost.php?p=3977517&postcount=3

See the comments about punctuation, and tex vs itex tags.