### Parity of the Spherical Harmonics

In spherical coordinates, the parity operation is

The radial part of the wavefunction, therefore, is unchanged and the

parity of the state is determined from the angular part. We know the state in general. A parity transformation gives.

The states are either even or odd parity depending on the quantum number .

The angular momentum operators are axial vectors and do not change sign under a parity transformation. Therefore, does not change under parity and all the with have the same parity as

Jim Branson 2013-04-22