Physlib.QuantumMechanics.Operators.OneDimension.Unbounded

An unbounded operator $U: S \to \mathcal{H}$ with domain embedding $\iota: S \to \mathcal{H}$ is symmetric (or formally self-adjoint) if for all $\psi_1, \psi_2 \in S$, the inner product in the Hilbert space $\mathcal{H}$ satisfies $\langle U \psi_1, \iota \psi_2 \rangle = \langle \iota \psi_1, U \psi_2 \rangle$. Here $\mathcal{H}$ is the 1D Hilbert space $L^2(\mathbb{R}, \mathbb{C})$.