If there are two light waves of same amplitude but of different frequencies then their energy will be same or different? If same then how will you define the light waves as photons and will there be a difference between the number of photons in both the Waves?
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I'm confused. Do you want to talk about classical field theory or QFT? Or are you asking for a comparison of the two? – Aug 27 '18 at 14:18
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See https://physics.stackexchange.com/q/27809/58651 – Jan Bos Aug 27 '18 at 15:58
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If you talk about amplitude of light wave I think, for example, about the electric field of the e.m. wave and, thus, the relation: $I = k \cdot |\vec{E^2}|$ and, supposing a sinusoidal electric field, you'll have: $I = k \cdot {E_0}^2 \cdot sin^2(\omega t)$, k real number (to enphasize the fact that it's not an equality but a proportionality more) and I intensity, E electric field.
Moreover, the energy density per unit area carried by this field is $\frac{1}{2} \cdot \epsilon_0 \cdot {E_0}^2$.
If you put same amplitude to the electric field but at different frequencies, you can see that in time they would have different intensity but they don't carry different energy. More intensity means that there is a larger number of photons.
But photons themselves can carry different energy par each because of this: $ E_{phot} = h\omega $ which makes you see the correlation between frequency and single-photon energy.
Costantino
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