- #1
advphys
- 17
- 0
Homework Statement
prove,
∇x(ψv)=ψ(∇xv)-vx(∇ψ)
using levi civita symbol and tensor notations
Homework Equations
εijkεimn=δjnδkm-δknδjm
The Attempt at a Solution
i tried for nth component
εnjk (d/dxj)εklm ψl vm
εknjεklm (d/dxj) ψl vm
using εijkεimn=δjnδkm-δknδjm
i got,
(d/dxj)ψn vj - (d/dxj)ψj vn
But, i can't go further. I think only one simple step is left to show it is equal to the right hand side of the given identity. But how?