The term "azimuthal quantum number" and "angular quantum number" are often used interchangeably to refer to the same concept in quantum mechanics. This quantum number is denoted by the symbol ℓ (lowercase letter "ell") and is associated with the angular momentum of a particle in a three-dimensional system.
The reason why it is called the "azimuthal quantum number" is because it is related to the azimuthal angle, which describes the orientation or direction of a vector in a plane. In the context of quantum mechanics, the azimuthal quantum number determines the magnitude of the angular momentum component of a particle along a particular axis or direction. It quantifies the orbital angular momentum of an electron in an atom.
On the other hand, the term "angular quantum number" is more general and encompasses both the azimuthal quantum number (ℓ) and the magnetic quantum number (mℓ). The magnetic quantum number specifies the projection of the angular momentum along a chosen axis. So when the term "angular quantum number" is used, it can refer to the azimuthal quantum number as well as the magnetic quantum number together.
To summarize, both "azimuthal quantum number" and "angular quantum number" refer to the same concept in quantum mechanics, but the former specifically relates to the azimuthal angle and the latter is a broader term that encompasses both the azimuthal and magnetic quantum numbers.