Take volume V with electro-magnetic field with classic energy (integral of E^2+H^2 ) , then make Fourie transform, then change variables and see, that field is simply the sum of (p^2 + w^2*x^2) for each harmonic = you have many oscillators (pendulums), and from quantum mechanic we know that energy of 1 oscilllator is hw.

Sorry for my quick English.

The reply of Pavel is essentially right. To see a sketch of the mathematical derivation, it is enough to consult the following Wikipedia page:

http://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field

and look for Hamiltonian of the field:

http://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field#Hamiltonian_of_the_field

There are some technical details, such as the specific gauge (Coulomb gauge). Then one has to apply the quantization rules for the Fourier coefficients.

The Wikipedia article also nicely explains the classical limit (as required by the question) with a simple example:

http://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field#Hamiltonian_of_the_field

An introduction to the scalar and vector potentials as tools for solving Maxwell's equation is in chapter 18-6 of the celebrated Feynman's Lectures on Physics (Volume II).

Finally, if you look for "second quantization electromagnetic field" in a search engine, you will be able to download many tutorials on the topic with even more details than the Wikipedia article. Here are two of them from coast to coast:

http://people.seas.harvard.edu/~jones/ap216/lectures/ls_3/ls3_u2/ls3_unit_2.pdf

http://www.stanford.edu/~rsasaki/AP387/chap3

Chris Papps

Loved Einstein's 1920 lecture at Leyden, and wished I had read it a decade before instead of being forced into the same conclusion myself through my research.

The aether Einstein described had nothing in common with the view put forth by Lorentz, other than it is a medium for wave propagation. Indeed it is close to the concept of the vacuum put forth much latter.

My work was on semi-classical educational models to introduce advanced physics concepts at the undergraduate level. I treated the vacuum as a perfect fluid in my models with great success. They give a mass for the Up and Down quarks within observed values, predicted that the energy plasmas in particle collisions would behave as a perfect fluid, recently confirmed, and also predicted the slightly smaller than classical size of the proton, also recently confirmed. Heck, my book were they were predicted was out of print before they were confirmed. I had to write a book as no one would publish my work, tried for a decade, just because I treated the vacuum as a medium.

Not bad predictions for semi-classical models no one would publish. I wish I had learned of the 1920 lecture ages ago, but the hatred of even the word aether is such it often ends careers, so not surprised I did not hear of it before.

We should be reasonable enough to look past a word and at the meaning behind it. The aether is just a name used as a medium for wave propagation. The vacuum in every respect acts as a medium, treat it as such.

Doing so worked well with my simple semi-classical models, imagine what a seasoned physicist could do if they could get past their hatred of a word and looked at results instead.