Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics

DOI10.1063/1.523120zbMath0342.22015OpenAlexW2086070869MaRDI QIDQ4109848

M. Perroud, Jirí Patera, Jules Beckers, Pavel Winternitz

Publication date: 1977

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.523120

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (15)

Continuous subgroups of a generalized Euclidean group ⋮ Pairs of commuting quadratic elements in the universal enveloping algebra of Euclidean algebra and integrals of motion* ⋮ Persistent manifolds of the special Euclidean group \(\mathrm{SE}(3)\): a review ⋮ Fiberwise homogeneous geodesic foliations of hyperbolic and Euclidean 3-spaces ⋮ On the Lie symmetry algebras of the stationary Schrödinger and Pauli equations ⋮ Symmetric subspaces of \(\mathrm{SE}(3)\) ⋮ On subalgebras of the Lie algebra of the extended Poincaré group P̃(1,n) ⋮ Optimal systems and group classification of \((1+2)\)-dimensional heat equation ⋮ Maximal abelian subalgebras of real and complex symplectic Lie algebras ⋮ Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups ⋮ The optical group and its subgroups ⋮ Inönü–Wigner contractions of the real four-dimensional Lie algebras ⋮ Classification of the space-times admitting a constant curvature synchronization ⋮ Subalgebras of real three- and four-dimensional Lie algebras ⋮ Subgroups of Lie groups and separation of variables

Cites Work

• Connected subgroups of the Poincaré group. I
• Subgroups of the similitude group of three-dimensional Minkowski space
• Broken Symmetries
• The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1)
• Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré group
• Symmetry and separation of variables for the Helmholtz and Laplace equations
• Symmetry breaking interactions for the time dependent Schrödinger equation
• The Group $O(4)$, Separation of Variables and the Hydrogen Atom
• Subgroups of the Poincaré group and their invariants
• Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0
• On the automorphisms of real Lie algebras
• Some applications of the representation theory of the Euclidean group in three‐space
• Group Theoretical Discussion of Relativistic Wave Equations
• Enumeration of Potentials for Which One-Particle Schroedinger Equations Are Separable

This page was built for publication: Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics