Why "textbook examples" of solutions to Schrodinger equation only deal with electrons? Whenever studying first courses of quantum mechanics, the Schrodinger eqaution is always illustrated by an electron in some kind of a potential, and the solution (wavefunction) represents probability. But is it possible for example to solve the Schrodinger equation for a quarks (proton) - electron system? Or instead of solving for an electron in the potential of a proton, is it possible to solve for a proton in a potential of an electron?
 A: The Schrodinger equation is an approximation because it ignores relativistic effects and it ignores spin. However, aside from these limits it applies to any system and not just electrons. The trouble is that the Schrodinger equation, and indeed most partial differential equations, are impossible to solve except in a few special cases. Since we have no special desire to melt the brains of new students we generally start by describing those special cases.
The solutions for electrons are a convenient starting point for various reasons. Electrons are light, so we can approximate them as moving in static potential e.g. in an atom or molecule we the nuclei are so much heavier than electrons that we assume they are fixed in place when calculating the electron wavefunction. Most of chemistry can be explained by just calculating the wavefunctions for electrons moving around static nuclei. We can also get a pretty accurate answer by treating the electrons as moving in an average potential, so we reduce an insoluble many body problem to an approximately soluble single body problem.
If we take your example of a nucleus, this is a very difficult problem. The strong force that holds nuclei together can't be described by a non-relativistic equation. Even if it we ignore the detail and use some approximate potential for the strong force, we have a many body system that isn't amenable to the sorts of simplifications we can use in atoms. In fact a full description of the structure of nuclei is beyond us even using our most advanced theories.
