Question

Visualizations of hydrogen's wavefunctions / electron orbitals are abound.

I could not however locate a visualization of the wavefunction of a proton. The reason I was looking for one is to see whether the three quarks that make it up "occupy" disjoint regions of space (i.e. the maximum probability locations are separated).

Can someone please point to one such visualization, or explain why they can't be created (or why my question is nonsensical, which is always a possibility...)

Answer 1

for the electron in the Hydrogen atom, the orbital motion doesn't interact with the electron's spin, so "the wave function" pretty much means just a complex . You may choose the electron's spin to be up or down independently of that.

However, you must realize that a wave function of three quarks has many more components. First of all, there are three particles in relative motion rather than two. It means that even if you decouple the center-of-mass coordinates, the relative wave function is a function of six coordinates,

So you can't really visualize the full wave function in a simple way because it is a function of six variables rather than three and of course, it doesn't factorize into a product of functions of three variables (something that is strictly speaking true even for all atoms more complicated than the Hydrogen atom).

Moreover, you must understand that the quarks have many discrete degrees of freedom that are not decoupled from the orbital motion in this case. Each of the three quarks has 1 of 3 colors and 1 of 2 possible values of the spin. The combinations of the color really force you to consider 27 combinations of the quark colors - 27 different wave functions (only 6 of them are nonzero and equal to each other, up to a sign) - and 8 combinations of the three quarks' spin. The spins are correlated as well.

So the right wave function for 3 quarks is really a set of 27