Intensity of light and energy at a photonic level

Question

If I understand correctly, the intensity of light is proportional to the number of photons hitting a certain area. If we then look at a single photon when described as a transverse wave, is its own energy equal to the square of the amplitude of that photon's wave? If we have a high energy photon this would mean the amplitude would be large, and the converse for a low energy wave.

Answer 1

Photons are quantized excitations of the electromagnetic field. The physical properties of a photon are encoded in the possible eigenvalues of the observables expressed in terms of the associated field operators. The full agreement between theory and experiments witnesses the correctness of such a description.

Such a preliminary statement would like to stress that we cannot extend the classical description of electromagnetic waves to photons without checking if it is consistent with the theoretical description of the photon or with some experimental evidence. Neither theory nor decades of experiments show that assigning a wave to a single photon is possible.

The energy of a monochromatic photon is nothing but its frequency times the Planck constant.

Answer 2

If I understand correctly, the intensity of light is proportional to the number of photons hitting a certain area.

The intensity of light is proportional to the number of photons and their energy content.

If we then look at a single photon when described as a transverse wave, is its own energy equal to the square of the amplitude of that photon's wave?

According to current understanding, the oscillating magnetic and electric field components of the light quantum extend infinitely far. A single photon therefore has no amplitude.

If we have a high energy photon this would mean the amplitude would be large, and the converse for a low energy wave.

A high-energy photon has a higher energy content and an amplitude (height of the wave crest/valley) is not meaningful.