Look, prof. Zaslavsky is completely correct.  But.  The great mathematician Jean Leray once, after being asked to think about Maslov's work on asymptotic methods to approximate the solutions of partial differential equations which were generalisations of the WKB method, decided, in the 70's, to write an entire book titled
*The meaning of Maslov's asymptotic method: The need of Planck's constant in mathematics.*

This is not a derivation of the magnitude of Planck's constatnt from Maxwell's equations, but it is a profound motivation for why there should be some finite, small, constant such as Planck's from the standpoint that the caustics you get in geometrical optics cannot be physical, and yet geometric optics *ought* to be a useful approximation to wave optics.  From this point of view, there *ought* to be some constant like Planck's constant, at least in pure mathematics.