Quasiclassical and Quantum Systems of Angular Momentum. Part III. Group Algebra of $\mathrm{SU}(2)$, Quantum Angular Momentum and Quasiclassical Asymptotics

Abstract

This is the third part of our series "Quasiclassical and Quantum Systems of Angular Momentum". In two previous parts we have discussed the methods of group algebras in formulation of quantum mechanics and certain quasiclassical problems. Below we specify to the special case of the group $\mathrm{SU}(2)$ and its quotient $\mathrm{SO}(3,\mathbb{R})$, and discuss just our main subject in this series, i.e., angular momentum problems. To be more precise, this is the purely $\mathrm{SU}(2)$-treatment, so formally this might also apply to isospin. However. it is rather hard to imagine realistic quasiclassical isospin problems.

References in corpus (4)

• Quantized excitations of internal affine modes and their influence on Raman spectra
• Quasiclassical and Quantum Systems of Angular Momentum. Part II. Quantum Mechanics on Lie Groups and Methods of Group Algebras
• Quasiclassical and Quantum Systems of Angular Momentum. Part I. Group Algebras as a Framework for Quantum-Mechanical Models with Symmetries
• Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics