Orbital Angular Momentum

orbital angular momentum [′ȯr·bəd·əl ′aŋ·gyə·lər mə′men·təm]

(mechanics)

The angular momentum associated with the motion of a particle about an origin, equal to the cross product of the position vector with the linear momentum. Also known as orbital momentum.

(quantum mechanics)

The angular momentum operator associated with the motion of a particle about an origin, equal to the cross product of the position vector with the linear momentum, as opposed to the intrinsic spin angular momentum. Also known as orbital moment.

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Orbital Angular Momentum 

the angular momentum of a microparticle moving in a strong field that has spherical symmetry. The term “orbital angular momentum” is due to the graphic representation of the motion of an atomic electron in a spherically symmetric field of the nucleus in a definite closed orbit.

According to quantum mechanics, the orbital angular momentum M_I is quantized, that is, its value, as well as its projection on an axis arbitrarily selected in space (z-axis), can assume only certain discrete values:

where h̷ is Planck’s constant, l = 0, 1, 2, …is the azimuthal (orbital) quantum number, and m = l, l — 1, … , — l is the magnetic quantum number. The classification of the states of microparticles according to the values of l plays a major role in atomic theory, in the theory of the atomic nucleus, and in collision theory.

M. A. EL’IASHEVICH