Spherical harmonics for Schrodinger equation

Spherical harmonics are special mathematical functions defined on the angular coordinates, the azimuthal and polar angles, phi and theta, as shown in the box. Why are spherical harmonics important in quantum mechanics? As we will see, the spherical harmonics make up part of the electron’s wavefunctions in a hydrogen atom. Just like the spatial and time harmonics we have seen earlier are consequences of the spatial and time translation symmetry, the spherical harmonics is a consequence of the rotational symmetry of the hydrogen problem. In this video, we shall review how the spherical harmonics solutions is obtained, and how one can visualize them.
Technical Content: Tony Low
Video Production: Katie Low, Tony Low
Erratum.
In 2.22, the angles \phi and \theta in the equations on the right should be interchanged. Thanks to ‪@cinemaclips4497‬ for pointing out this typo.