For some parts of physics it is useful to define an operator valued function
Take for example
R[K_] := Sum[K[[j]] D[#, K[[j]]], {j, 1, 4}]
It is supposed to be an operator and I placed a # where the function should be, to which the operator will be applied to i.e.
R[K]&@F[K[[1]],...]
It is important however, that R remains a function of the parameters only. That means that the result of R[K] is still an operator. The way, I created the operator does not work, do you now, how to do it?
Do you know in particular, how one could write the above operator as a scalar product where one vector consists of
K={a,b,c,d}
and the other is a Vectoroperator
DEL={$\partial_t$,$\partial_x$,$\partial_y$,$\partial_z$}
such that one can take e.g.
((K.DEL)+1) &@ f
I am happy about every hint.
