224 citations · 812 across the 39 of their papers we have counts for
39 papers
Four-body (an)harmonic oscillator in -dimensional space: -states, (quasi)-exact-solvability, hidden algebra
M. A. Escobar-Ruiz, Alexander V. Turbiner, Willard Miller
As a generalization and extension of our previous paper {\it J. Phys. A: Math. Theor. 53 055302} \cite{AME2020}, in this work we study a quantum 4-body system in ($d…
A new way to classify 2D higher order quantum superintegrable systems
Bjorn K. Berntson, Ian Marquette, Willard Miller
We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schrödinger eigenvalue equation $HΨ\equiv…
Classical -body system in geometrical and volume variables. I. Three-body case
A. M. Escobar-Ruiz, R. Linares, Alexander V Turbiner +1
We consider the classical 3-body system with degrees of freedom at zero total angular momentum. The study is restricted to potentials that depend solely on relative…
Toward Classification of 2nd Order Superintegrable Systems in 3-Dimensional Conformally Flat Spaces with Functionally Linearly Dependent Symmetry Operators
Bjorn K. Berntson, Ernest G. Kalnins, Willard Miller
We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD)…
From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics
Alexander V Turbiner, Willard Miller, M. Adrian Escobar-Ruiz
It is shown that planar quantum dynamics can be related to 3-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case…
Three-body closed chain of interactive (an)harmonic oscillators and the algebra
Alexander V Turbiner, Willard Miller, Adrian M Escobar-Ruiz
In this work we study 2- and 3-body oscillators with quadratic and sextic pairwise potentials which depend on relative distances, , between particles. The…