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.
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.
Oops my bad, it’s been a while. I thought the Hamiltonian used quaternions, but I guess that’s just complex numbers.
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.