Angular momentum and spin in quantum mechanics

Ajit Kumar

V Hnizdo

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin–orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the rate of change of the spin, the particle's total angular momentum in which the orbital angular momentum is defined in terms of the kinetic momentum is generally not conserved. However, a generalized total angular momentum, in which the orbital part is defined in terms of the canonical momentum, is conserved. This illustrates the fact that the quantum-mechanical operator of momentum corresponds to the canonical momentum of classical mechanics.

K. Heyde

V. T. Davis

Angular momentum is essential to any advanced discussion of magnetic resonance spectroscopy. A brief history of the modern sub-atomic particle-spin concept is presented. The origin of the spin-1/2 angular momentum quantum number is detailed and angular momentum operators are constructed for spin-1/2 nuclei using the postulates of quantum mechanics which are then used to produce a set of very useful eigenvalue formulas. Angular momentum operators in spherical coordinate form are developed and operator matrices are constructed from Cartesian operators. The time-evolution of these operators is of much interest in later chapters and is explored in some detail here.

Angular momentum is essential to any advanced discussion of magnetic resonance spectroscopy. A brief history of the modern sub-atomic particle-spin concept is presented. The origin of the spin-1/2 angular momentum quantum number is detailed and angular momentum operators are constructed for spin-1/2 nuclei using the postulates of quantum mechanics that are then used to produce a set of very useful eigenvalue formulas. Angular momentum operators in spherical coordinate form are developed and operator matrices are constructed from Cartesian operators. The time-evolution of these operators is of much interest in later chapters and is explored in some detail here.