The very first thing my textbook says is that the Del operator is defined as: $$\vec{\nabla}=\vec{a}^i\nabla_i$$ Where $\nabla_i$ is the covariant derivative and " $\vec{a}^i$ is the curvilinear basis of the curvilinear coordinates $\xi ^i$". However I can't understand if that should be the dual basis (because of the upper index) or it is just written that way to obey einstein notation (upper and lower repeating) or maybe it is a mistake (I don't believe it to be). Can you help me clarify this?
$\begingroup$
$\endgroup$
13
asked Oct 21, 2023 at 15:23
-
1$\begingroup$ What textbook?? $\endgroup$– DanielCCommented Oct 21, 2023 at 15:35
-
$\begingroup$ Is this supposed to be the Hamiltonian operator in quantum mechanics? $\endgroup$– P. C. SpanielCommented Oct 21, 2023 at 15:44
-
$\begingroup$ Have you explored the gradient in spherical coordinates? $\endgroup$– Cosmas ZachosCommented Oct 21, 2023 at 16:01
-
$\begingroup$ DanielC "Лекции по векторно и тензорно смятане за физици" It's in Bulgarian $\endgroup$– Krum KutsarovCommented Oct 21, 2023 at 16:15
-
1$\begingroup$ I've never heard of it being called a Hamilton operator. Me neither. $\endgroup$– GhosterCommented Oct 21, 2023 at 17:27
|
Show 8 more comments