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1. Parity Reversal

   Linked via "unitary"

   $$\mathcal{P} | \mathbf{r} \rangle = | -\mathbf{r} \rangle$$
   In quantum mechanics, the parity operator is unitary ($\mathcal{P}^\dagger \mathcal{P} = \mathcal{I}$) and its square is the identity ($\mathcal{P}^2 = \mathcal{I}$), meaning the eigenvalues of $\mathcal{P}$ are restricted to $+1$ (even parity) or $-1$ (odd parity).
   The relationship between parity and momentum is defined by the commutation relation: