How to know if a spinor $Psileft(xright)$ is the ground state of the system?

Suppose we have time independent one-dimensional single particle Schrödinger-like equation$$-frac{d}{dx}left(Aleft(xright)frac{d}{dx}psileft(xright)right)+Vleft(xright)psileft(xright)=Epsileft(xright),$$
where $Aleft(xright)$ is a positive function. We have guessed an eigenfunction $psi_{mathrm{guess}}left(xright)$ of energy $E_{mathrm{guess}}$, and wonder if this is the ground state of the system.

I know two methods we can use in order to check if $psi_{mathrm{guess}}left(xright)$ is the ground state of the system:

1. If $psi_{mathrm{guess}}left(xright)$ has no nodes, than it is the ground state.
2. If we can write the Hamiltonian in the form of $H=E_0 + varepsilon a^{dagger}a$, and $E_{mathrm{guess}}$ happens to be equal to $E_0$, than $psi_{mathrm{guess}}left(xright)$ is the ground state.

My question is about a spinor analog of this. Suppose we have time independent one-dimensional Schrödinger equation for spin $s$ particle$$-frac{d}{dx}left(Aleft(xright)frac{d}{dx}Psileft(xright)right)+Vleft(xright)Psileft(xright)=EPsileft(xright),$$
where $Aleft(xright)$ is a positive-defined $(2s+1)times (2s+1)$ hermitian matrix, and $Vleft(xright)$ is a $(2s+1)times (2s+1)$ hermitian matrix. We again guessed an eigenspinor $Psi_{mathrm{guess}}left(xright)$ of energy $E_{mathrm{guess}}$, and wonder if this is the ground state of the system.

Method $(2)$ I metioned above should still work, but looks like it is mostly impracticle. Is there a generaliztion of method $(1)$, or of some other method, that can help solving the problem?