According to the standard interpretation of quantum mechanics, the amplitude of a single photon is generally considered to be fixed and equal to one unit. In this interpretation, the amplitude is related to the probability of detecting the photon at a specific location or exhibiting a particular behavior.
The energy of a photon is indeed determined by its frequency. The energy of a photon is directly proportional to its frequency and is given by the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency.
However, it's important to note that quantum mechanics allows for fluctuations and uncertainties in various quantities, including the amplitude. These uncertainties are described by the wave function, which provides a probabilistic description of the behavior of quantum particles.
In practice, experimental measurements of single photons can have some inherent noise and uncertainty due to various factors such as detection limitations, environmental conditions, or technical constraints. These factors can introduce small perturbations or fluctuations in the observed properties of individual photons, including their amplitude. However, on average, the amplitude of a large number of photons of the same frequency will be approximately constant.
It's worth noting that the precise nature of quantum mechanics and the behavior of individual photons are still areas of active research, and different interpretations and experimental techniques may provide further insights and refinements in the future.