Thanks TW, ohh yes I now start to understand a little, I am novice on wave functions and operators. Yes I see the regular wave function is a scalar

so possibly I could switch to div operator as then get scalar ?

\begin{equation}

- \frac{\partial \Psi}{\partial t}=- \nabla\cdot(\Psi \textbf{c})

\end{equation}

I am not sure this gives meaning, is consistent, or even if my notation is right...I need to study more here, any good book on "vector and scalar operators for novices in 24 hours" ?
(PS my erroneous wave equation do not alter my analysis on de Broglie versus Compton etc and the momentum etc, but yes my wave equation not properly derived)..
Also I am still wondering about the imaginary numbers in the standard wave function \(e^{i....}\) (that I borrowed from standard QM), is it somehow also linked to the Old Mystical formula?
"Thus the essence of this postulate can be expressed mathematically very concisely in the mystical formula: \(3\times 10^5 \mbox{ km} =\sqrt{-1}\) seconds" Henry Minkowski (we are living in the mystical esoteric age of physics

tw:

It was only a trivial observation but for you is psi a scalar function? (as in a regular wavefunction).

partial psi/partial t is then a scalar, but grad(psi) is a vector?

The advection equation uses div.