Suppose one considers "classical Quantum Theory": we work in a Hilbert space $\mathbb{C}^n$ with standard inner product $\langle \cdot \vert\cdot \rangle$, etc. The nonzero vectors in $\mathbb{C}^n$ correspond to states. What is the physical meaning of states $\vert \psi \rangle$ for which $\langle \psi \vert \psi \rangle = 0$, that is, self-orthogonal states ?
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