I recently read an answer and I was not able to make sense of it. The answer said Let us consider the famous double-slit experiment with photons. With the usual set-up, we denote the number of photons passing through by N and we will denote the number of photons which hit the film between y and y+Δy by n(y). The probability that a photon will be detected between y and y+Δy at a time t is given by: Py(y,t)≡limN→∞(n(y)N) If we consider this from an classical electromagnetic point of view, then the above quantity is known as the intensity I of the electromagnetic wave which is well known to be proportional to: I(y,t)∝|ψ(y,t)|2Δy
Now I did not understand why the probability is what is given in the answer so if someone could clarify that and why is that a probability. If the interference pattern is observed what do u mean by probability,the photon is there isn't it. And secondly why is the probability equal to the intensity of the pattern. I am just beginning Quantuam Mechanics and I am not able to understand this .