Physlib.QuantumMechanics.Operators.OneDimension.Parity

The unbounded parity operator $P$ defined on the domain of Schwartz functions $\mathcal{S}(\mathbb{R}, \mathbb{C}) \subset L^2(\mathbb{R}, \mathbb{C})$, which maps a function $\psi(x)$ to $\psi(-x)$, is symmetric. That is, for all Schwartz functions $\phi, \psi \in \mathcal{S}(\mathbb{R}, \mathbb{C})$, the $L^2$ inner product satisfies $\langle \phi, P\psi \rangle = \langle P\phi, \psi \rangle$.