 Spatial reflection

Here spatial reflection means inversion of all three spatial coordinates, $\mathbf{r}\mapsto -\mathbf{r}$, as used in the parity operator. This differs geometrically from reflection in a single plane, which reverses only the perpendicular coordinate. In three dimensions inversion reverses orientation; in two dimensions simultaneous reversal of both coordinates is instead a half-turn.

Under three-dimensional inversion, a position or momentum vector changes sign, while angular momentum $\mathbf{L}=\mathbf{r}\times \mathbf{p}$ does not. This distinction explains why angular momentum is an axial vector. In quantum mechanics, inversion tests the parity of a wavefunction and whether a Hamiltonian exhibits parity conservation.