Spherical Harmonics in Atomic Orbitals and Magnetic Fields

In this video, I go over an overview of how spherical harmonics show up in the equations for atomic orbitals and magnetic fields. The Schrödinger equation is a partial differential equation that governs the wave function that mathematically describes a quantum state. Solutions to the Schrödinger equation are standing waves called stationary states or energy eigenstates or "atomic orbitals". I go over the Schrödinger equation for the electron in a hydrogen atom, which is also applicable to hydrogen-like atoms (any atom or ion with a single electron), and the corresponding solution that involves spherical harmonics. Similarly, I show that the spherical harmonics arise also in the equation of magnetic fields, which are derived from the mathematical scalar potential function.

#math #sphericalharmonics #calculus #atomicphysics #magnet