[muawiyah]

Just a note: the probability of large waves occurring is a function of the number of smaller waves. Not so long ago when a ship was swamped or went down as a result of wave action people who wanted to finish out their nautical careers in peace kept their mouths shut about it.

Then, finally, the rogue waves were found, and they weren't as rogue as once thought ~ in fact, they are quite predictable ~ today we have computers analyzing satellite images to see if they are out and about.

What a change.

Now, keep that mind as we revisit your statement about ".... That quantity, called the expectation value, is vanishingly small for classical particles ....." ~ no doubt you've had to think about this in the past so what is the explanation for classical wave forms? (understanding that all those particles are themselves waves of some kind, and in various manners linked together).

Can we change the functions that create the columbe barrier in virtually any wave form? Or are we simply stuck with condensed states of matter as suggested by Widom and Larsen?

Seems to me that if we can sink a large ship with simple wave functions we should be able to stuff a proton or two inside a hydrogen nucleus, right?

[chimera]

I'm not sure the analogy is valid. Formation of ocean waves is simply a matter of fluid mechanics. Remember that quantum theory is best applied at the subatomic level. Classical mechanics works fine for the macroscopic world. It isn't that quantum theory is invalidated. Its just that its effects are more observably manifest on small distance scales. Trying to apply it at classical scales is pretty much a useless exercise, because the quantum effects become vanishingly small, at least in terms of observability.

As far as "stuffing protons inside a hydrogen nucleus", remember that a hydrogen nucleus in its most common form is simply a proton, so the "stuffing into a nucleus" becomes more a problem of simply joining another particle. This is difficult with a charged particle like another proton, but it can be done if you have enough energy. Fusion reactions that are done in things like tokamaks and the older-style stellators used D-D or D-T reactions. I used to run D-D reactions all the time in a simple linear accelerator when I was a physics student. It was a source of relatively energetic neutrons. We also ran D-T reactions with a tritiated target and a deuteron beam. That produces 14 MeV neutrons. The simplest nucleus beyond hydrogen is the deuteron, wherein a neutron is "joined" to a proton. It is just barely stable. A little bit of added energy (relatively speaking) will separate them.