Calogero-like Model without Rearrangement Symmetry
Abstract
:1. Introduction
2. Spectral Degeneracy and Its Unfolding at A = 2
2.1. Singularity in the Origin
2.2. Asymmetric Barrier
3. Spectral Degeneracy and its Unfolding at A = 3
3.1. Weyl Chambers
3.2. Nonequal Barriers vs. Loss of Solvability
3.3. Reinstallation of Solvability: Asymmetric Barriers
4. Spectral Degeneracy and Its Unfolding Beyond A = 3
4.1. Exact Solvability
4.2. Weyl-Chamber Boundaries and Their Cartography at A = 4
4.2.1. Colorings at
4.2.2. Projection on a Central Sphere
4.2.3. Projections on a Central Cube
4.2.4. Numbering by Permutations
4.3. Alternative Cartography at A = 4
4.3.1. Projections of the Set of Weyl Chambers on a Tetrahedron
4.3.2. An Ultimate Classification of the Barriers
5. Summary
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. The Occurrence of Asymmetric Impenetrable Barriers in Relativistic Quantum Mechanics
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Znojil, M. Calogero-like Model without Rearrangement Symmetry. Symmetry 2024, 16, 27. https://doi.org/10.3390/sym16010027
Znojil M. Calogero-like Model without Rearrangement Symmetry. Symmetry. 2024; 16(1):27. https://doi.org/10.3390/sym16010027
Chicago/Turabian StyleZnojil, Miloslav. 2024. "Calogero-like Model without Rearrangement Symmetry" Symmetry 16, no. 1: 27. https://doi.org/10.3390/sym16010027
APA StyleZnojil, M. (2024). Calogero-like Model without Rearrangement Symmetry. Symmetry, 16(1), 27. https://doi.org/10.3390/sym16010027