The nature of particles in quantum mechanics can be described by wave functions, which represent the probability distributions of their properties. In the case of protons, the wave function describes the behavior of the particle in terms of its position, momentum, and other observable properties.
While wave functions describe the probabilistic nature of particles, they do not directly explain the origin of particle mass or the specific way particles are composed. The concept of mass arises from the interaction of particles with the Higgs field in the Standard Model of particle physics.
According to the current understanding in particle physics, protons are composite particles made up of three quarks (two up quarks and one down quark) bound together by the strong force mediated by gluons. This is known as the quark model.
The mass of a proton does not arise solely from the masses of the three constituent quarks. In fact, the masses of the up and down quarks are relatively small compared to the mass of a proton. The majority of the proton's mass comes from the energy associated with the strong force that binds the quarks together, as well as the contributions from the virtual particles and the Higgs mechanism.
The gluons, which carry the strong force, mediate the interactions between the quarks within the proton. The strong force is responsible for confining the quarks within a bound state and giving rise to the overall properties of the proton, such as its mass and charge.
So, while wave functions describe the probabilistic behavior of particles, they do not provide a direct explanation for the mass or the composite nature of particles like protons. The mass of a proton arises from a combination of the masses of its constituent quarks, the energy of the strong force that binds them, and other factors within the framework of the Standard Model of particle physics.