# How is it that Increase in amplitude of electromagnetic radiation results in increase in number of photons

I cannot comprehend how the increasing of amplitude of an electromagnetic wave increases the number of photons. How does this even happen. I am also not able able to make sense of that fact that, when you increase frequency, you increase the energy of each individual photon. How does this happen? Is there a better way to visualize this

• May 25 at 8:25
• The second statement is a direct postulate of Planck's Quantum Theory. Perhaps you can visualise this in the way that a highly energetic particle will be able to make rapid oscillations and hence have a higher frequency. May 25 at 11:02
• I very rarely think about changing the energy or count of photons once they exist, only what they are when generating the photons. Is there a situation you are specifically concerned about where you change the energy or count of existing photons?
– Matt
May 25 at 19:58

$$\mathrm{P}\!\cdot\!\mathrm{t} = h\nu n$$
Where P is the power of the source, n is the no of photons, h is plank's constant and $$\nu$$ is frequency of incident electromagnetic radiation.
The state with definite photon number will have uncertain amplitude, whereas a state with well-dfeined amplitude (a coherent state) will have high uncertainty in the photon number. One however can calculate this uncertainty, which is given by a Poissonian distrubution (see here), and for high amplitudes proportional to the field intensity: $$(\Delta n)^2\propto E^2$$