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Physlib.QuantumMechanics.Operators.OneDimension.Unbounded

Unbounded operators

Note

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1 declaration

definition

Symmetry of an unbounded operator UU (formally self-adjointness)

An unbounded operator U:S→HU: S \to \mathcal{H} with domain embedding ι:S→H\iota: S \to \mathcal{H} is symmetric (or formally self-adjoint) if for all ψ1,ψ2∈S\psi_1, \psi_2 \in S, the inner product in the Hilbert space H\mathcal{H} satisfies ⟨Uψ1,ιψ2⟩=⟨ιψ1,Uψ2⟩\langle U \psi_1, \iota \psi_2 \rangle = \langle \iota \psi_1, U \psi_2 \rangle. Here H\mathcal{H} is the 1D Hilbert space L2(R,C)L^2(\mathbb{R}, \mathbb{C}).