Let us consider a nonrelativistic particle of mass $m$, spin $s$ and isospin $i$. The Schrodinger equation for the state vector $|\psi(t)\rangle$ of this particle is given by
$$i\hbar\frac{d|\psi(t)\rangle}{dt} = \hat{H}|\psi(t)\rangle \, , $$
where $\hat{H}$ is the Hamiltonian operator and the other symbols have their usual meanings.
My questions are as follows.
- Is $|\psi(t)\rangle = |\phi(t)\rangle \otimes |\chi(t)\rangle \otimes |I(t)\rangle$ ?
Here, $|\phi(t)\rangle$, $|\chi(t)\rangle$ and $ |I(t)\rangle$ are the spatial, spin and isospin state vectors of the particle.
I have specified the time dependence of the state vectors by writing as, e.g., $ |I(t)\rangle$. Is that correct?
Say, the particle is relativistic. Then what would be the state vector? In other words, if the particle is relativistic, then other than the spatial, spin and isospin state vectors, what else should be included in $|\psi(t)\rangle$?
If you know any relevant reference for the answer, please mention that too.