Yes, according to quantum mechanics, all elementary particles, including protons and neutrons, can be described by wave functions. The wave function of a particle provides information about the probability distribution of finding the particle at different locations in space.
However, there are some important differences between the wave functions of electrons and photons compared to protons and neutrons. Electrons and photons are elementary particles that are inherently quantum mechanical in nature, meaning their wave-like behavior is more prominent. Their wave functions describe the probability distributions of their positions or momenta.
Protons and neutrons, on the other hand, are composite particles made up of quarks and gluons. While they do have associated wave functions, the wave-like behavior is less pronounced at macroscopic scales compared to electrons or photons. The wave function of a proton or neutron describes the probability distribution of the positions of the constituent quarks and gluons, as well as their relative configurations within the particle.
The wave functions of protons and neutrons are typically described within the framework of quantum chromodynamics (QCD), which is the theory governing the strong nuclear force. Due to the complex interactions among the quarks and gluons, solving the QCD equations to obtain the wave function of a proton or neutron is a highly challenging task.
In practical terms, when dealing with macroscopic objects like protons and neutrons, their wave functions are often not explicitly considered or calculated. Instead, we use statistical models and approximations to describe their behavior in certain contexts, such as in nuclear physics or particle physics experiments.
It's worth noting that the wave functions of protons, neutrons, electrons, and photons all play a crucial role in understanding the behavior of matter and radiation at the quantum level. However, the specific mathematical descriptions and interpretations of their wave functions differ based on the nature and properties of the particles.