Under this question and answer discussion- https://physics.stackexchange.com/a/187562/297159 , how more than one photon can be absorbed by 1 electron has been explained briefly. However, if multi-photon absorption is possible, it means that the particle nature of light , like the wave nature, gives a continuous absorption of energy. What is then the point of the particle nature theory? There remains no difference, because the one-to-one interaction is the very basis of the particle nature theory. We have learnt that since the wave nature couldn’t explain the photoelectric effect the non continuous energy absorption’s idea was suggested by the particle nature theory. But if particle nature allows continuous energy absorption then what’s the point of the theory? Can someone please explain this?
But if particle nature allows continuous energy absorption then what’s the point of the theory?
"more than one" does not mean "continuous". Discrete counting cannot be turned into "continuous" energy values.
At the quantum level the energy is not absorbed or emitted by the electron, but by the whole atom, so it is not improbable that the combined system of two photons interacting with the atom as discussed in the link you give. It just means that the energy of two photons can be absorbed to ionize an atom. Two does not mean continuous.