Physics · Quantum Mechanics

Consider a spin-1 system whose Ŝz eigenstates are given by |-1⟩, |0⟩, |+1⟩ corresponding to the eigenvalues -ℏ, 0, ℏ respectively. A normalized general state |ψ⟩ of the system is expressed as |ψ⟩ = c-1|-1⟩ + c0|0⟩ + c+1|+1⟩, where c-1, c0, c+1 are complex numbers. If the state satisfies the condition ⟨ψ|Ŝz|ψ⟩ = 0, which of the following statements must be true?