Chapter 11 is devoted to the quantum theory of angular momentum. As in classical mechanics, working with angular momentum requires leaving the one-dimensional space, with all the complications that this entails. The importance of angular momentum resides in at least three facts: i) central problems are of particular interest; (ii) many particles have an intrinsic angular momentum (the spin); and iii) the physics of angular momentum involves features such as the so-called space quantization. The first part of the chapter deals with the orbital angular momentum and its eigenfunctions, the spherical harmonics. Its algebraic properties, embodied in the matrix representation, allow for an extension of the theory to half-integer angular momentum in terms of Pauli matrices, as well as the addition of angular momenta.Chapter 11 is devoted to the quantum theory of angular momentum. As in classical mechanics, working with angular momentum requires leaving the one-dimensional space, with all the complications that this entails. The importance of angular momentum resides in at least three facts: i) central problems are of particular interest; (ii) many particles have an intrinsic angular momentum (the spin); and iii) the physics of angular momentum involves features such as the so-called space quantization. The first part of the chapter deals with the orbital angular momentum and its eigenfunctions, the spherical harmonics. Its algebraic properties, embodied in the matrix representation, allow for an extension of the theory to half-integer angular momentum in terms of Pauli matrices, as well as the addition of angular momenta.

Cambridge University Press eBooksDec 18, 20250 citations

Large quantum probability backflow and the azimuthal angle–angular momentum uncertainty relation for an electron in a constant magnetic field

P. Strange

In this paper we demonstrate a surprising aspect of quantum mechanics that is accessible to an undergraduate student. We discuss probability backflow for an electron in a constant magnetic field. It is shown that even for a wavepacket composed entirely of states with negative angular momentum the effective angular momentum can take on positive values in some regions of space. This is also a demonstration of the azimuthal angle–angular momentum uncertainty relation. This example is chosen because the backflow motion persists indefinitely. However this work can easily be extended to other systems where the motion is notionally circular, such as the hydrogen atom.In this paper we demonstrate a surprising aspect of quantum mechanics that is accessible to an undergraduate student. We discuss probability backflow for an electron in a constant magnetic field. It is shown that even for a wavepacket composed entirely of states with negative angular momentum the effective angular momentum can take on positive values in some regions of space. This is also a demonstration of the azimuthal angle–angular momentum uncertainty relation. This example is chosen because the backflow motion persists indefinitely. However this work can easily be extended to other systems where the motion is notionally circular, such as the hydrogen atom.

European Journal of PhysicsJul 2, 201229 citations

Unveiling Angular Momentum

Stephen Paul Robinson

Bulletin of the American Physical SocietyMar 4, 20150 citations

Direct Demonstration of Spin-Angular-Momentum Conservation in the Reaction He(2S12)+He(2S13)→He(1S01)+He++e−

J. C. Hill, Lynn L. Hatfield, N. D. Stockwell +1 more

Conservation of spin angular momentum in the reaction $\mathrm{He}(2^{2}S_{1})+\mathrm{He}(2^{3}S_{1})\ensuremath{\rightarrow}\mathrm{He}(1^{1}S_{0}+{\mathrm{He}}^{+}+{e}^{\ensuremath{-}}$ is demonstrated quantitatively in the afterglow of a helium discharge by measuring the dependence of the electron production rate upon $2^{3}S_{1}$ spin-state populations, which are manipulated by an optical-pumping technique.Conservation of spin angular momentum in the reaction $\mathrm{He}(2^{2}S_{1})+\mathrm{He}(2^{3}S_{1})\ensuremath{\rightarrow}\mathrm{He}(1^{1}S_{0}+{\mathrm{He}}^{+}+{e}^{\ensuremath{-}}$ is demonstrated quantitatively in the afterglow of a helium discharge by measuring the dependence of the electron production rate upon $2^{3}S_{1}$ spin-state populations, which are manipulated by an optical-pumping technique.

Physical Review AJan 1, 197237 citations

Some simple angular momentum techniques

John P. Killingbeck

Physics Letters ADec 1, 19771 citation

2^{3}S_{1}

spin-state populations, which are manipulated by an optical-pumping technique.