Quantum versus classical angular momentum

• Published in: European journal of physics Vol. 41; no. 2; pp. 25402 - 25414
• Main Authors: Mostowski, Jan, Pietraszewicz, Joanna
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.03.2020
• Subjects: angular momentum; classical limit of quantum mechanics; Clebsch-Gordan coefficients
• ISSN: 0143-0807; 1361-6404
• DOI: 10.1088/1361-6404/ab4b2d

Angular momentum in classical mechanics is given by a vector. The plane perpendicular to this vector, in accordance to central field theory, determines the space in which particle motion takes place. No such simple picture exists in quantum mechanics. The states of a particle in a central field are proportional to spherical harmonics which do not define any plane of motion. In the first part of this paper we discuss the angular distribution of particle position and compare it to the classical probabilistic approach. In the second part, the matter of addition of angular momenta is discussed. In classical mechanics this means addition of vectors, while in quantum mechanics Clebsch-Gordan coefficients have to be used. We have found classical approximations to quantum coefficients and the limit of their applicability. This analysis gives a basis for the so-called 'vector addition model' used in some elementary textbooks on atomic physics. It can help to better understand the addition of angular momenta in quantum mechanics.