The Hamiltonian using Hamilton's numbers? Now I think about it it is a bit silly that two entirely separate yet highly propinquitous concepts have such similar names. Physics really went downhill once humans started writing it down.
I know this is a joke, but wrong about what, exactly? I don't get it.
Also, and maybe this has something to do with the joke I'm not getting, the way complex numbers are motivated in school is a lie, and a stupid one. Mathematicians were perfectly comfortable with certain equations having no solutions; the problem was when their equations told them there were no solutions when they could see the solutions: the curve x3 - 15x + 4 crosses the x-axis, but Cardano's cubic formula gives up due to negative square roots. Imaginary numbers were originally no more than an ephemeral reasoning tool, and were only reluctantly accepted as entities in their own right because of how damn useful they were.
Quaternions are not the basis for quantum mechanics. Biquaternions have some applications in quantum field theory, but there are many areas of quantum mechanics where there's no need or space for anything above complex.
The Hamiltonian using Hamilton's numbers? Now I think about it it is a bit silly that two entirely separate yet highly propinquitous concepts have such similar names. Physics really went downhill once humans started writing it down.