Quantum Mechanical Theory of Orbital Angular Momentum

Jean-Marc Lévy-Leblond

A. C. Sharma

This chapter covers various aspects of orbital, total, and spin angular momenta and the Clebsch-Gordon coefficients. An approach that is not found in many books, is used to derive eigenvalues of orbital angular momentum. The Pauli theory of spin half systems, addition of angular momenta, eigenfunctions of orbital angular momentum, computation of Clebsch-Gordon coefficients, solved examples, and unsolved exercises are included in the chapter. The basic purpose of the chapter has been to bring out the quantum mechanical importance of the theory of angular momenta with the use of essential mathematical derivations, which are self-consistent, and to adopt an elegant modern approach. Special mention on why orbital angular momentum cannot have non-integer values is made. The concept of spin angular momentum, which is purely a quantum mechanical quantity, is introduced in a simple and most convincing manner.

Daniel Charles Mattis

Gordon Baym

The orbital angular momentum of a particle in quantum mechanics is defined exactly as in classical mechanics. Before developing any properties of the angular momentum operators, students must know the commutation relations they satisfy with themselves, with the momentum operator, and with the position operator. The angular momentum operator is very closely related to rotations of the system. Students should compare the ability of the angular momentum operator to generate infinitesimal rotations, with the corresponding property of the linear momentum p. The chapter provides the theory of the orbital angular momentum sufficiently to study the problem of a particle in a central potential.

Dmitry A. Varshalovich, A.N. Moskalev, V. K. Khersonskii

Javier Silvestre

Bohr atomic model is developed with electronic extremes of Victoria Theory. Toyi mechanism is focused on explaining orbital angular and spin movement of electronic extremes. This article summarizes first part of Toyi Mechanism and then proceeds with individualized explanation of angular momentum for all orbitals (named as Fluyiep Explanation). Finally, paper concludes with fundamental relations between angular momentum of all orbitals.