Preface – This post is part of the Quantum Computing series.

In quantum mechanics, angular momentum is a physical property that describes the rotational motion of a particle or system. It is closely related to the concept of angular momentum in classical mechanics, but it has some important differences due to the principles of quantum mechanics.

In classical mechanics, angular momentum is defined as the product of an object’s mass, its velocity, and its distance from a fixed point (known as the moment of inertia). Angular momentum is a vector quantity, which means it has both a magnitude and a direction. In quantum mechanics, angular momentum is also a vector quantity, but it is quantized, which means that it can only take on certain discrete values.

The quantization of angular momentum is a consequence of the wave-particle duality of quantum systems. Quantum systems can exhibit both wave-like and particle-like properties, and the angular momentum of a quantum system is determined by its wave function, which describes the probability of finding the system at a given position and orientation.

The angular momentum of a quantum system is described by its angular momentum operator, which is a mathematical operator that acts on the system’s wave function to determine its angular momentum. The angular momentum operator is closely related to the position and momentum operators, which describe the position and momentum of a quantum system.

Angular momentum is an important concept in quantum mechanics because it plays a role in many phenomena, including the structure of atoms and molecules, the behavior of particles in magnetic fields, and the quantum states of particles with spin. It is also an important tool for understanding the symmetries of quantum systems, and it is used to classify the quantum states of particles and systems.