In electromagnetism, there is a notion called "Poynting vector."

It represents an electromagnetic energy flow current in vacuum space.

It is defined as a vector product of electric field E and magnetic field H.

That is,

S=ExH

In quantum mechanics, the electromagnetic wave is represented by the broadly prevailing notion of photon.

A photon has a definite energy hv.

The Poynting vector is well defined function of position and time, that is, S=S(x,y,z,t).

On the contrary, the quantum mechanical photon is ill defined regarding its position and time. It says only the energy the photon possesses.

Then here come my questions to you.

Is there anyone who can connect the above two kind of physical notions?

Is there anyone who can bridge the gap between the two features of light?

Regarding the Schrodinger equation: "There is no derivation of this equation. There is no proof of this equation. Scientists use this equation because it is useful." from page 9 of http://courses.chem.psu.edu/chem408/reading/activities/activity_2_QM.pdf

Schrodinger proposed his equation based on Max Plank's successful idea of quantum oscillators, which Plank modeled as masses on springs absorbing and re-emitting radiation. Plank did that in order to accurately predict the emission spectrum of a "black body emitter" such as a red hot iron or oven. The notion of quantum oscillators absorbing and re-emitting radiation would best be investigated at the source: Plank's paper on quantum oscillators.

The most cutting edge branch of this is currently Density Function Theory: Density functional theory - Wikipedia, the free encyclopedia