They are just saying that (by definition),Muthumanimaran said:
Ah, but then 3.1.13 follows directly from 3.1.11 with the choice ## f(a) = a^m## and ## f(a^\dagger) = (a^\dagger)^n##. That's all there is to it. I am not sure what the question is, then.Muthumanimaran said:
The Sudarshan-Glauber P function is a mathematical function used in quantum optics to describe the probability of detecting a certain number of photons in a particular mode of light. It was first introduced by E. C. G. Sudarshan and Roy J. Glauber in 1963.
The Sudarshan-Glauber P function is derived using the principles of quantum mechanics and the concept of coherent states. It involves performing a transformation on the quantum state of a light field, which results in a classical distribution of photon number probabilities.
The Sudarshan-Glauber P function is widely used in the field of quantum optics for various applications, such as studying the statistics of light in optical systems, characterizing non-classical states of light, and analyzing the behavior of light in quantum measurements.
The Sudarshan-Glauber P function differs from other photon distribution functions, such as the Poisson and Gaussian distributions, in that it takes into account the quantum nature of light. It can accurately describe the statistics of light in both classical and non-classical regimes.
One limitation of the Sudarshan-Glauber P function is that it assumes the light field to be in a coherent state, which may not always be the case in practical situations. It also does not take into account the effects of losses and imperfections in the optical system, which can affect the accuracy of the derived results.
