On particular integrability in classical mechanics - IOPscience Skip to content IOP Science
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Taking the Hydrogen atom as an example it is shown that if the symmetry of a three-
dimensional system is O (2)⊕ Z 2, the variables (r, ρ, φ) allow a separation of the variable φ …

A study is presented of superintegrable quantum systems in two-dimensional Euclidean
space E 2 allowing the separation of variables in Cartesian coordinates. In addition to the …

In this work we study 2-and 3-body oscillators with quadratic and sextic pairwise potentials
which depend on relative distances,, between particles. The two-body harmonic oscillator is …

We construct a rational extension of the truncated Calogero–Sutherland model by Pittman et
al. The exact solution of this rationally extended model is obtained analytically and it is …

The primary purpose of this note is to prove two recent conjectures concerning the n body
matrix that arose in recent papers of Escobar-Ruiz, Miller, and Turbiner on the classical and …

A simple locally accurate uniform approximation for the nodeless wave function is
constructed for a neutral system of two Coulomb charges of different masses (− q, m 1) and …

Helium-like ions in d-dimensions: analyticity and generalized ground state Majorana solutions
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Due to its great importance for applications, we generalize and extend the approach of our
previous papers to study aspects of the quantum and classical dynamics of a 4-body system …

As a generalization and extension of our previous paper [Turbiner et al., J. Phys. A: Math.
Theor. 53, 055302 (2020)], in this work, we study a quantum four-body system in R d (d≥ 3) …