Publications

Integrability and Superintegrability of Hamiltonian Systems

with M. A. Quiroz-Juarez, J. L. Del Rio-Correa and N. Aquino, Classical harmonic three-body system: an experimental electronic realization, Scientific Reports volume 12, 13346 (2022)
with I. Yurdusen and Irlanda Meza y Palma, Doubly Exotic Nth-order Order Superintegrable Classical Systems Separating in Cartesian Coordinates, SIGMA 18 (2022), 039, 20 pages
with R. Linares, P. Winternitz, New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates, accepted manuscript to appear in J. Phys. A: Math. Theor. (2020)
with A. V. Turbiner, W. Miller Jr., From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics, J. Phys. A: Math. Theor. 54 (2020) 015204
with A. V. Turbiner, W. Miller Jr., Three-body closed chain of interactive (an)harmonic oscillators and the algebra sl(4;R), J. Phys. A: Math. Theor. 53 (2020) 055302
with P. P. Goldstein, A. M. Grundland, The su(2) spin s representations via CP^{2s} sigma models, J. Phys. Commun. 4 (2020) 105006
with J. C. Ndogmo, Equivalence classes and Linearization of the Riccati and Abel chain, Journal of Mathematical Analysis and Applications, 475 (2019) 1818-1830
with P. Winternitz, _I. Yurdusen General N^th-order superintegrable systems separating in polar coordinates, J. Phys. A: Math. Theor. 51 (2018) 40LT01
with J. C. López Vieyra, P. Winternitz, _I. Yurdusen Fourth order superintegrable systems separating in Polar Coordinates. II. Standard Potentials, J. Phys. A: Math. Theor. 51 (2018) 455202
with J. C. López Vieyra, P. Winternitz, Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials, J. Phys. A: Math. Theor. 50 (2017) 495206
with W. Miller Jr., E. Subag, Contractions of degenerate quadratic algebras, abstract and geometric, SIGMA 13 (2017) 099
with E. G. Kalnins, W. Miller Jr., Separation equations for 2D superintegrable systems on constant curvature spaces, J. Phys. A: Math. Theor. 50 (2017) 385202
with E. G. Kalnins, W. Miller Jr., E. Subag, Bôcher and abstract contractions of 2nd order quadratic algebras, SIGMA 13 (2017) 013
with W. Miller Jr., Toward a classification of semidegenerate 3D superintegrable systems, J. Phys. A: Math. Theor. 50 (2017) 095203
with W. Miller Jr., Conformal Laplace superintegrable systems in 2D: polynomial invariant subspaces, J. Phys. A: Math. Theor. 49, (2016), 305202

Many body problem

with Alexander V. Turbiner, Classical n-body system in volume variables II: Four-body case, International Journal of Modern Physics A 37 (2022) 2250209
with R. Linares, Alexander V. Turbiner and Willard Miller Jr., Classical n-body system in geometrical and volume variables I: Three-body case, International Journal of Modern Physics A 36 (2021) 2150140
with W. Miller Jr., A. V. Turbiner, Four-body (an)harmonic oscillator in d-dimensional space: S-states, (quasi)-exact-solvability, hidden algebra sl(7), Journal of Math Physics 62 (2021) 072103
with W. Miller Jr., A. V. Turbiner, Four-body problem in d-dimensional space: ground state, (quasi)-exact-solvability. IV, Journal of Math Physics 60 (2019) 062101
with W. Miller Jr., A. V. Turbiner, The quantum n-body problem in dimension d > n – 1: ground state, J. Phys. A: Math. Theor. 51 (2018) 205201
with A. V. Turbiner, W. Miller Jr., Three-body problem in d-dimensional space: ground state, (quasi)-exact-solvability, Journal of Math Physics 59 (2018) 022108
with C. A. Escobar Three charges on a plane in a magnetic field: Special trajectories, Journal of Math Physics 59 (2018) 102901
with A. V. Turbiner, W. Miller Jr., Three-body problem in 3D space: ground state, (quasi)-exact-solvability, J. Phys. A: Math. Theor. 50 (2017) 215201

Path integral (instanton calculus)

Perturbative and variational methods in quantum mechanics

Casimir Effect

Corrigendum

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