David Bohm's Paper on Hidden Variables Theory

[The_Inventor]

So I've been reading David Bohm's original paper on the alternative interpretation of quantum mechanics in terms of hidden variables, just out of interest. In the 4th section he presents a complex function ψ in terms of R and S, and then (using the time dependent Schrödinger equation, TISE) gives the partial derivatives of R and S with respect to time. My problem is I can't seem to work out how he did it. The thing I did was to use the chain rule and to take the derivative of ψ with respect to R and S, and then multiply those with the derivatives of R and S with respect to time, respectively. However, from there I got lost because after plugging these back into the TISE, I couldn't seem to simplify the relation to resemble the one in the paper, perhaps there is some laplacian identity that I'm unaware of, or some algebraic manipulation that I can't see. Can anyone help me out??

(I have linked the original paper to this post for reference, page 4 is what my question is on.)
http://fma.if.usp.br/~amsilva/Artigos/p166_1.pdf

 

[Demystifier]

The functions $R$ and $S$ are useful because they are real (not complex like $\Psi$). So when you plug everything back to the TDSE, and multiply the whole expression with $\Psi^*$ to remove the common phase factor $e^{iS/\hbar}$, you should observe that the resulting equation has two kinds of terms. The ones that are purely real, and the ones that are purely imaginary. This means that the complex TDSE is really two equations, one for the real part and another for the imaginary part. Write down those two equations separately and you should obtain (3) and (4).