explain in detail

Explain in detail 120 years of evidence for quantum mechanics? If I write five hundred thousand words on the history and development of quantum mechanics, will you read them all or stop after the first sentence?

We would probably start with wave interference and the photoelectric effect:

• wave interference demonstrates that light behaves as a wave capable of interference and cancellation;
• the photoelectric effect demonstrates that light behaves as discrete particles;
• so light is simultaneously both wave-like and particle-like;
• particles of matter, starting with single electrons and going all the way up to giant molecules made up of 2000 atoms each, also demonstrate wave behaviour
• hence matter itself is also simultaneously wave-like and particle-like.

From there go on to the ultraviolet collapse of the atom in classical mechanics and emission/absorption spectra:

• under classical mechanics, an accelerating electric charge will generate electromagnetic radiation, causing it to lose energy
• so the electrons in the atom would spiral into the central nucleus, giving up all their energy in an almost instantaneous burst of ultraviolet radiation;
• emission and absorption spectra show that radiation can only be emitted and absorbed by atomic electrons in discrete, discontinuous amounts;
• thus solving the problem of the ultraviolet catastrophe but showing that electrons do not have well-defined orbits but rather wave-like orbitals.

That's just the beginning. But the bottom line is that at the scale of atoms, matter behaves as waves, not point-like particles or tiny solid spheres. Mapping those wave functions which spread out to infinity under quantum mechanics to the localised values that we measure occurs probabilistically:

• the wave function spreads out over a volume
• but our measurements always give us a specific value within that volume, with some probability as given by quantum mechanics.

I'm not saying that with quantum mechanics we have reached the end of science and the Ultimate Truth Of The Universe. We still don't know how to reconcile quantum mechanics with gravity and general relativity. It is always possible that the future will bring in a paradigm shift that will change our understanding of wave interference etc.

Nor am I quite ruling out some sort of hidden variable theory that would eliminate the need for wave functions to be interpreted as "probability waves". But such hidden variables would have to violate relativity.