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Interference pattern made by light shows the wave nature of light and photoelectric effect shows

particle nature of light. So, what is light?

According to the photoelectric effect, light consists of photons with energy E and momentum ## \vec

p##.

According to the interference pattern, we don't know where an individual particle will reach on the screen.

So, considering one-dimensional case, what I understood is that there is a wave - function ## \psi (x,t) ## associated with each photon such that ## |\psi|^2 dx ## tells us the probability of finding the particle in the region dx at time t. So, if a particle reaches x at time t then it can be said that the particle has momentum ## \vec p ## and energy E at x and t. Thus, it is meaningless to say that the particle has momentum ## \vec p ## and energy E without specifying its position and time.

Thus, what we can say is the probability of finding the particle with momentum ## \vec p ## and

energy E in dx at time t. Thus, the probability of finding the energy of particle to be E in region dx at time t should be given as E ## |\psi|^2 dx ##.

I don't understand why the author is emphasizing that ## \psi ## is associated with each particle, not a collection of particles.