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Often a hydronium ion H₃O⁺ attaches itself to *three* other water molecules, forming H₉O₄⁺.

This is called an 'Eigen cation', named after Manfred Eigen, a famous chemist who has nothing to do with eigenvectors.

Even this isn't the end of the story. More and more water molecules can surround a lone proton, forming larger and larger structures. And thanks to quantum mechanics, the extra proton's wavefunction can spread out over the whole structure! It naturally does that, to lower its energy.

Let's see an example.

(4/n)