On the incompleteness of the classification of quadratically integrable Hamiltonian systems in the three-dimensional Euclidean space
Year: 2025
Type: article
Abstract: We present an example of an integrable Hamiltonian system with scalar potential in the three-dimensional Euclidean space whose integrals of motion are quadratic polynomials in the momenta, yet its Hamilton–Jacobi / Schrödinger equation cannot separate in any orthogonal coordinate system. This demonstrates a loophole in the derivation of the list of quadratically integrable Hamiltonian systems in Makarov et al (1967 Nuovo Cimento A 10 1061–84) where only separable systems were found, and the need for its revision.
Author: Libor Šnobl
Institution: Czech Technical University in Prague
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
Award: G487403935
OpenAlex ID: W4408230958