Everything about Angular Momentum Operator totally explained
In
quantum mechanics, the
angular momentum operator is an
operator analogous to classical
angular momentum. The angular momentum operator plays a central role in the theory of
atomic physics and other quantum problems involving
rotational symmetry. In both classical and quantum mechanical systems, angular momentum (together with linear momentum and energy) is one of the three fundamental properties of motion.
Intuitive meaning
Angular momentum quantifies the rotational aspect of motion. Like energy and linear momentum, angular momentum in an isolated system is conserved. The concept of an angular momentum
operator is necessary in quantum mechanics, as calculations of angular momentum must be made upon a
wave function, rather than on a point or rigid body as classical calculations entail. This is because at the scale of quantum mechanics, the
matter analyzed is best described by a wave equation or
probability amplitude, rather than as a collection of fixed points or as a rigid body.
Vector calculus is used in calculations of angular momentum, as angular momentum has compenents in each of the three spatial dimensions.
Mathematical definition
Angular momentum
L is mathematically defined as the
cross product of a wave function's
position operator (
r) and
momentum operator (
p):
»
are the
spherical harmonics.
Further Information
Get more info on 'Angular Momentum Operator'.
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