The University of Queensland

Higher order quantum superintegrability: a new “Painlevé Conjecture”: higher order quantum superintegrability

Marquette, Ian and Winternitz, Pavel (2019). Higher order quantum superintegrability: a new “Painlevé Conjecture”: higher order quantum superintegrability. Integrability, supersymmetry and coherent states: A Volume in Honour of Professor Véronique Hussin. (pp. 103-131) edited by Şengül Kuru, Javier Negro and Luis M. Nieto. Cham, Switzerland: Springer International Publishing. doi: 10.1007/978-3-030-20087-9_4

Polynomial algebras from Lie algebra reduction chains g ⊃ g ′

Campoamor-Stursberg, Rutwig, Latini, Danilo, Marquette, Ian and Zhang, Yao-Zhong (2023). Polynomial algebras from Lie algebra reduction chains g ⊃ g ′. Annals of Physics, 459 169496, 1-19. doi: 10.1016/j.aop.2023.169496

Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces

Marquette, Ian, Zhang, Junze and Zhang, Yao-Zhong (2023). Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces. Journal of Physics A: Mathematical and Theoretical, 56 (35) 355201, 355201. doi: 10.1088/1751-8121/ace949

The Lie algebra of the lowest transitively differential group of degree three

Grundland, Alfred Michel Michel and Marquette, Ian (2023). The Lie algebra of the lowest transitively differential group of degree three. Journal of Physics A: Mathematical and Theoretical, 56 (34) 345205, 345205. doi: 10.1088/1751-8121/ace866

Non-Hermitian superintegrable systems

Correa, Francisco, Inzunza, Luis and Marquette, Ian (2023). Non-Hermitian superintegrable systems. Journal of Physics A: Mathematical and Theoretical, 56 (34) 345207, 345207. doi: 10.1088/1751-8121/ace506

Infinite-dimensional representations of cubic and quintic algebras and special functions

Marquette, Ian, Zhang, Junze and Zhang, Yao-Zhong (2023). Infinite-dimensional representations of cubic and quintic algebras and special functions. European Physical Journal Plus, 138 (6) 537. doi: 10.1140/epjp/s13360-023-04155-2

Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras

Campoamor-Stursberg, Rutwig, Latini, Danilo, Marquette, Ian and Zhang, Yao-Zhong (2023). Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras. Journal of Physics A: Mathematical and Theoretical, 56 (4) 045202, 1-27. doi: 10.1088/1751-8121/acb576

On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials

Marquette, I. and Zelaya, K. (2022). On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials. Physica D: Nonlinear Phenomena, 442 133529, 1-10. doi: 10.1016/j.physd.2022.133529

Algebraic construction of associated functions of nondiagonalizable models with anharmonic oscillator complex interaction

Marquette, I. and Quesne, C. (2022). Algebraic construction of associated functions of nondiagonalizable models with anharmonic oscillator complex interaction. Reports on Mathematical Physics, 90 (3), 285-298. doi: 10.1016/s0034-4877(22)00077-5

Generalized quadratic commutator algebras of PBW-type

Marquette, Ian, Yates, Luke and Jarvis, Peter D. (2022). Generalized quadratic commutator algebras of PBW-type. Journal of Mathematical Physics, 63 (12) 121703, 1-23. doi: 10.1063/5.0096769

Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators

Latini, Danilo, Marquette, Ian and Zhang, Yao-Zhong (2022). Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators. Physica D: Nonlinear Phenomena, 440 133464, 1-20. doi: 10.1016/j.physd.2022.133464

Dynamical symmetry algebras of two superintegrable two-dimensional systems

Marquette, Ian and Quesne, Christiane (2022). Dynamical symmetry algebras of two superintegrable two-dimensional systems. Journal of Physics A: Mathematical and Theoretical, 55 (41) 415203. doi: 10.1088/1751-8121/ac9164

Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras

Latini, Danilo, Marquette, Ian and Zhang, Yao-Zhong (2022). Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras. Journal of Physics A: Mathematical and Theoretical, 55 (33) 335203, 1-42. doi: 10.1088/1751-8121/ac7ca3

A family of fourth-order superintegrable systems with rational potentials related to Painlevé VI

Marquette, I., Post, S. and Ritter, L. (2022). A family of fourth-order superintegrable systems with rational potentials related to Painlevé VI. Journal of Physics A: Mathematical and Theoretical, 55 (15) 155201. doi: 10.1088/1751-8121/ac550a

Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras

Campoamor-Stursberg, Rutwig and Marquette, Ian (2022). Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras. Annals of Physics, 437 168694, 168694. doi: 10.1016/j.aop.2021.168694

Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. I. two-dimensional model

Marquette, Ian and Quesne, Christiane (2022). Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. I. two-dimensional model. Symmetry, Integrability and Geometry: Methods and Applications, 18 004. doi: 10.3842/sigma.2022.004

Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. II. three-dimensional model

Marquette, Ian and Quesne, Christiane (2022). Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. II. three-dimensional model. Symmetry, Integrability and Geometry: Methods and Applications, 18 005, 1-24. doi: 10.3842/sigma.2022.005

Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials

Hussin, Veronique, Marquette, Ian and Zelaya, Kevin (2022). Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials. Journal of Physics A: Mathematical and Theoretical, 55 (4) 045205. doi: 10.1088/1751-8121/ac43cc

Racah algebra R(n) from coalgebraic structures and chains of R(3) substructures

Latini, Danilo, Marquette, Ian and Zhang, Yao-Zhong (2021). Racah algebra R(n) from coalgebraic structures and chains of R(3) substructures. Journal of Physics A: Mathematical and Theoretical, 54 (39) 395202, 395202. doi: 10.1088/1751-8121/ac1ee8

N-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra SW(N)

Correa, Francisco, Fazlul Hoque, Md, Marquette, Ian and Zhang, Yao-Zhong (2021). N-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra SW(N). Journal of Physics A: Mathematical and Theoretical, 54 (39) 395201, 395201. doi: 10.1088/1751-8121/ac1dc1

Non-linear ladder operators and coherent states for the 2:1 oscillator

Moran, James, Hussin, Véronique and Marquette, Ian (2021). Non-linear ladder operators and coherent states for the 2:1 oscillator. Journal of Physics A: Mathematical and Theoretical, 54 (27) 275301, 1-17. doi: 10.1088/1751-8121/ac0200

Embedding of the Racah algebra R(n) and superintegrability

Latini, Danilo, Marquette, Ian and Zhang, Yao-Zhong (2021). Embedding of the Racah algebra R(n) and superintegrability. Annals of Physics, 426 168397, 1-18. doi: 10.1016/j.aop.2021.168397

Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems

Campoamor-Stursberg, Rutwig and Marquette, Ian (2021). Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems. Annals of Physics, 424 168378, 168378. doi: 10.1016/j.aop.2020.168378

Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians

Zelaya, K., Marquette, I. and Hussin, V. (2020). Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians. Journal of Physics A: Mathematical and Theoretical, 54 (1) 015206, 1-29. doi: 10.1088/1751-8121/abcab8

Polynomial algebras from su(3) and a quadratically superintegrable model on the two sphere

Correa, F., del Olmo, M. A., Marquette, I. and Negro, J. (2020). Polynomial algebras from su(3) and a quadratically superintegrable model on the two sphere. Journal of Physics A: Mathematical and Theoretical, 54 (1) 015205, 1-16. doi: 10.1088/1751-8121/abc909

A fourth-order superintegrable system with arational potential related to Painlevé VI

Marquette, Ian, Post, Sarah and Ritter, Lisa (2020). A fourth-order superintegrable system with arational potential related to Painlevé VI. Journal of Physics A: Mathematical and Theoretical, 53 (50) 50LT01, 1-13. doi: 10.1088/1751-8121/abbf06

A new way to classify 2D higher order quantum superintegrable systems

Berntson, Bjorn Karl, Marquette, Ian and Miller, Willard (2020). A new way to classify 2D higher order quantum superintegrable systems. Journal of Physics A: Mathematical and Theoretical, 53 (49) 494003, 1-21. doi: 10.1088/1751-8121/abc04a

The general Racah algebra as the symmetry algebra of generic systems on pseudo–spheres

Kuru, Sengul, Marquette, Ian and Negro, Javier (2020). The general Racah algebra as the symmetry algebra of generic systems on pseudo–spheres. Journal of Physics A: Mathematical and Theoretical, 53 (40) 405203, 405203. doi: 10.1088/1751-8121/abadb7

Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras

Chen, Zhe, Marquette, Ian and Zhang, Yao-Zhong (2019). Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras. Annals of Physics, 411 167970. doi: 10.1016/j.aop.2019.167970

Generalized conformal pseudo-Galilean algebras and their Casimir operators

Campoamor-Stursberg, Rutwig and Marquette, Ian (2019). Generalized conformal pseudo-Galilean algebras and their Casimir operators. Journal of Physics A: Mathematical and Theoretical, 52 (47) 475202, 1-17. doi: 10.1088/1751-8121/ab4c81

Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator

Hoffmann, Scott E., Hussin, Véronique, Marquette, Ian and Zhang, Yao-Zhong (2019). Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator. Journal of Mathematical Physics, 60 (5) 052105, 052105. doi: 10.1063/1.5091953

Two-dimensional superintegrable systems from operator algebras in one dimension

Marquette, Ian, Sajedi, Masoumeh and Winternitz, Pavel (2019). Two-dimensional superintegrable systems from operator algebras in one dimension. Journal of Physics A: Mathematical and Theoretical, 52 (11) 115202, 115202. doi: 10.1088/1751-8121/ab01a2

Extended Laplace-Runge-Lentz vectors, new family of superintegrable systems and quadratic algebras

Chen, Zhe, Marquette, Ian and Zhang, Yao-Zhong (2019). Extended Laplace-Runge-Lentz vectors, new family of superintegrable systems and quadratic algebras. Annals of Physics, 402, 78-90. doi: 10.1016/j.aop.2019.01.009

On Casimir operators of conformal Galilei algebras

Alshammari, Fahad, Isaac, Phillip S. and Marquette, Ian (2019). On Casimir operators of conformal Galilei algebras. Journal of Mathematical Physics, 60 (1) 013509, 013509. doi: 10.1063/1.5064840

Extended Calogero models: a construction for exactly solvable kN-body systems

Chen, Zhe, Links, Jon, Marquette, Ian and Zhang, Yao-Zhong (2018). Extended Calogero models: a construction for exactly solvable kN-body systems. Journal of Physics A: Mathematical and Theoretical, 51 (45) 455203, 455203. doi: 10.1088/1751-8121/aae4cc

Coherent states for ladder operators of general order related to exceptional orthogonal polynomials

Hoffmann, Scott E., Hussin, Veronique, Marquette, Ian and Zhang, Yao-Zhong (2018). Coherent states for ladder operators of general order related to exceptional orthogonal polynomials. Journal of Physics A: Mathematical and Theoretical, 51 (31) 315203, 315203. doi: 10.1088/1751-8121/aacb3b

Quantum superintegrable system with a novel chain structure of quadratic algebras

Liao, Yidong, Marquette, Ian and Zhang, Yao-Zhong (2018). Quantum superintegrable system with a novel chain structure of quadratic algebras. Journal of Physics A: Mathematical and Theoretical, 51 (25) 255201. doi: 10.1088/1751-8121/aac111

Recurrence approach and higher order polynomial algebras for superintegrable monopole systems

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2018). Recurrence approach and higher order polynomial algebras for superintegrable monopole systems. Journal of Mathematical Physics, 59 (5) 052101, 052101. doi: 10.1063/1.5012859

Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

Hoque, Md. Fazlul, Marquette, Ian, Post, Sarah and Zhang, Yao-Zhong (2018). Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials. Annals of Physics, 391, 203-215. doi: 10.1016/j.aop.2018.02.008

Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials

Hoffmann, Scott E., Hussin, Veronique, Marquette, Ian and Zhang, Yao-Zhong (2018). Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials. Journal of Physics A-Mathematical and Theoretical, 51 (8) 085202, 1-16. doi: 10.1088/1751-8121/aaa553

A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras

Alshammari, Fahad, Isaac, Phillip S. and Marquette, Ian (2018). A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras. Journal of Physics A: Mathematical and Theoretical, 51 (6) 065206, 065206. doi: 10.1088/1751-8121/aaa468

Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials

Marquette, Ian, Sajedi, Masoumeh and Winternitz, Pavel (2017). Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials. Journal of Physics A: Mathematical and Theoretical, 50 (31) 315201, 315201. doi: 10.1088/1751-8121/aa7a67

Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang–Coulomb monopole interaction

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2017). Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang–Coulomb monopole interaction. Annals of Physics, 380, 121-134. doi: 10.1016/j.aop.2017.03.003

Quadratic algebra for superintegrable monopole system in a Taub-NUT space

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2016). Quadratic algebra for superintegrable monopole system in a Taub-NUT space. Journal of Mathematical Physics, 57 (9) 092104, 092104. doi: 10.1063/1.4962924

Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

Marquette, Ian and Quesne, Christiane (2016). Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial. Journal of Mathematical Physics, 57 (5) 052101, 052101. doi: 10.1063/1.4949470

Recurrence approach and higher rank cubic algebras for the N-dimensional superintegrable systems

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2016). Recurrence approach and higher rank cubic algebras for the N-dimensional superintegrable systems. Journal of Physics A: Mathematical and Theoretical, 49 (12) 125201, 1-12. doi: 10.1088/1751-8113/49/12/125201

Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum

Isaac, Phillip S. and Marquette, Ian (2016). Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum. Journal of Physics A: Mathematical and Theoretical, 49 (11) 115201, 1-13. doi: 10.1088/1751-8113/49/11/115201

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⊕ so(n) ⊕ so(N-n)

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2015). A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⊕ so(n) ⊕ so(N-n). Journal of Physics A: Mathematical and Theoretical, 48 (Art No.: 445207) 445207, 273-&. doi: 10.1088/1751-8113/48/44/445207

Exact solution of the p+IP Hamiltonian revisited: Duality relations in the hole-pair picture

Links, Jon, Marquette, Ian and Moghaddam, Amir (2015). Exact solution of the p+IP Hamiltonian revisited: Duality relations in the hole-pair picture. Journal of Physics A: Mathematical and Theoretical, 48 (37) 374001, 1-22. doi: 10.1088/1751-8113/48/37/374001

New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization

Bagchi, Bijan and Marquette, Ian (2015). New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization. Physics Letters, Section A: General, Atomic and Solid State Physics, 379 (26-27), 1584-1588. doi: 10.1016/j.physleta.2015.04.009

Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

Marquette, Ian and Quesne,Christine (2015). Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions. Journal of Mathematical Physics, 56 (6) 062102, 062102-1-062102-19. doi: 10.1063/1.4922020

Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2015). Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension. Journal of Physics A: Mathematical and Theoretical, 48 (18) 185201, 1-16. doi: 10.1088/1751-8113/48/18/185201

Ground-state Bethe root densities and quantum phase transitions

Links, Jon and Marquette, Ian (2015). Ground-state Bethe root densities and quantum phase transitions. Journal of Physics A: Mathematical and Theoretical, 48 (4) 045204, 1-15. doi: 10.1088/1751-8113/48/4/045204

Combined state-adding and state-deleting approaches to type III multi-step rationally extended potentials: applications to ladder operators and superintegrability

Marquette, Ian and Quesne, Christiane (2014). Combined state-adding and state-deleting approaches to type III multi-step rationally extended potentials: applications to ladder operators and superintegrability. Journal of Mathematical Physics, 55 (11) 112103, 112103-1-112103-25. doi: 10.1063/1.4901006

New quasi-exactly solvable class of generalized isotonic oscillators

Agboola, Davids, Links, Jon, Marquette, Ian and Zhang, Yao-Zhong (2014). New quasi-exactly solvable class of generalized isotonic oscillators. Journal of Physics A: Mathematical and Theoretical, 47 (39) 395305, 395305.1-395305.17. doi: 10.1088/1751-8113/47/39/395305

On realizations of polynomial algebras with three generators via deformed oscillator algebras

Isaac, Phillip S. and Marquette, Ian (2014). On realizations of polynomial algebras with three generators via deformed oscillator algebras. Journal of Physics A: Mathematical and Theoretical, 47 (20) 205203, 1-26. doi: 10.1088/1751-8113/47/20/205203

New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems

Marquette, Ian and Quesne, Christiane (2013). New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems. Journal of Mathematical Physics, 54 (10) 102102, 102102-1-102102-12. doi: 10.1063/1.4823771

Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

Marquette, Ian (2013). Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras. Journal of Mathematical Physics, 54 (7) 071702, 071702.1-071702.15. doi: 10.1063/1.4816086

Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators

Marquette, I. and Quesne, C. (2013). Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators. Journal of Physics A: Mathematical and Theoretical, 46 (15) 155201, 155201. doi: 10.1088/1751-8113/46/15/155201

New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

Marquette, Ian and Quesne, Christiane (2013). New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials. Journal of Mathematical Physics, 54 (4) 042102, 042102-1-042102-16. doi: 10.1063/1.4798807

Integrability of an extended d+id-wave pairing Hamiltonian

Marquette, Ian and Links, Jon (2013). Integrability of an extended d+id-wave pairing Hamiltonian. Nuclear Physics B, 866 (3), 378-390. doi: 10.1016/j.nuclphysb.2012.09.006

Singular isotonic oscillator, supersymmetry and superintegrability

Marquette, Ian (2012). Singular isotonic oscillator, supersymmetry and superintegrability. Symmetry Integrability and Geometry: Methods and Applications, 8 063. doi: 10.3842/SIGMA.2012.063

Generalized Heine-Stieltjes and Van Vleck polynomials associated with two-level, integrable BCS models

Marquette, Ian and Links, Jon (2012). Generalized Heine-Stieltjes and Van Vleck polynomials associated with two-level, integrable BCS models. Journal of Statistical Mechanics: Theory and Experiment, 2012 (8) P08019, P08019. doi: 10.1088/1742-5468/2012/08/P08019

Generalized five-dimensional Kepler system, Yang-Coulomb monopole, and Hurwitz transformation

Marquette, Ian (2012). Generalized five-dimensional Kepler system, Yang-Coulomb monopole, and Hurwitz transformation. Journal of Mathematical Physics, 53 (2) 022103, 022103.1-022103.12. doi: 10.1063/1.3684955

Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems

Marquette, Ian (2012). Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems. Journal of Mathematical Physics, 53 (1) 012901, 012901.1-012901.12. doi: 10.1063/1.3676075

Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators

Marquette, Ian (2011). Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators. Journal of Physics A-Mathematical and Theoretical, 44 (23) 235203, 235203.1-235203.12. doi: 10.1088/1751-8113/44/23/235203

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

Marquette, Ian (2011). Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems. Journal of Mathematical Physics, 52 (4) 042301, 042301-1-042301-12. doi: 10.1063/1.3579983

Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras

Marquette, Ian (2010). Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras. Journal of Mathematical Physics, 51 (10) 102105, 102105-1-102105-10. doi: 10.1063/1.3496900

Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

Marquette, Ian (2010). Construction of classical superintegrable systems with higher order integrals of motion from ladder operators. Journal of Mathematical Physics, 51 (7) 037006JMP, 072903-1-072903-9. doi: 10.1063/1.3448925

Superintegrability and higher order polynomial algebras

Marquette, Ian (2010). Superintegrability and higher order polynomial algebras. Journal of Physics A - Mathematical and Theoretical, 43 (13) 135203, 135203-1-135203-15. doi: 10.1088/1751-8113/43/13/135203

Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion

Marquette, Ian (2009). Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion. Journal of Mathematical Physics, 50 (12) 122102, 122102-1-122102-10. doi: 10.1063/1.3272003

Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painleve transcendent potentials

Marquette, Ian (2009). Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painleve transcendent potentials. Journal of Mathematical Physics, 50 (9), 095202-1-095202-18. doi: 10.1063/1.3096708

Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials

Marquette, Ian (2009). Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials. Journal of Mathematical Physics, 50 (1), 012101-1-012101-23. doi: 10.1063/1.3013804

Superintegrable systems with third-order integrals of motion

Marquette, Ian and Winternitz, Pavel (2008). Superintegrable systems with third-order integrals of motion. Journal of Physics A - Mathematical and Theoretical, 41 (30) 304031, 304031-1-304031-10. doi: 10.1088/1751-8113/41/30/304031

Erratum : Polynomial poisson algebras for classical superintegrable systems with a third order integral of motion (vol 48, art no 012902, 2007)

Marquette, I. and Winternitz, P. (2008). Erratum : Polynomial poisson algebras for classical superintegrable systems with a third order integral of motion (vol 48, art no 012902, 2007). Journal of Mathematical Physics, 49 (1) 019901, 019901. doi: 10.1063/1.2831929

Polynomial Poisson algebras for superintegrable systems with a third order integral of motion

Marquette, Ian and Winternitz, Pavel (2007). Polynomial Poisson algebras for superintegrable systems with a third order integral of motion. Journal of Mathematical Physics, 48 (1), 012902.1-012902.16. doi: 10.1063/1.2399359

A New Approach to Analysis of 2D Higher Order Quantum Superintegrable Systems

Berntson, Bjorn K., Marquette, Ian and Miller, Willard (2020). A New Approach to Analysis of 2D Higher Order Quantum Superintegrable Systems. 11th International Symposium on Quantum Theory and Symmetries, Montreal, Canada, 1-5 July 2019. Cham, Switzerland: Springer. doi: 10.1007/978-3-030-55777-5_10

Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras

Marquette, Ian (2019). Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras. 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018, Prague, Czech Republic, 9-13 July, 2018. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/1194/1/012074

Coherent states for rational extensions and ladder operators related to infinite-dimensional representations

Hoffmann, Scott E., Hussin, Véronique, Marquette, Ian and Zhang, Yao-Zhong (2019). Coherent states for rational extensions and ladder operators related to infinite-dimensional representations. XXVI International Conference on Integrable Systems and Quantum symmetries, Prague, Czech Republic, 8–12 July 2019. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/1416/1/012013

On superintegrable monopole systems

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2018). On superintegrable monopole systems. 25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017, Prague, Czech Republic, 6-10June 2017. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/965/1/012018

Family of N-dimensional superintegrable systems and quadratic algebra structures

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2016). Family of N-dimensional superintegrable systems and quadratic algebra structures. 23rd International Conference on Integrable Systems and Quantum Symmetries, ISQS 2015, Prague, Czech Republic, 23 - 27 June 2015. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/670/1/012024

New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies

Marquette, Ian (2015). New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies. 30th International Colloquium on Group Theoretical Methods in Physics (Group30), Ghent, Belgium, 14-18 July 2014. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/597/1/012057

An infinite family of superintegrable systems from higher order ladder operators and supersymmetry

Marquette, Ian (2011). An infinite family of superintegrable systems from higher order ladder operators and supersymmetry. GROUP 28 Conference: XXVIIIth International Colloquium on Group-Theoretical Methods in Physics (ICGTMP), Newcastle upon Tyne, United Kingdom, 26–30 July 2010. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/284/1/012047

Generalized Heisenberg algebras, SUSYQM and degeneracies: Infinite well and Morse potential

Hussin, Veronique and Marquette, Ian (2011). Generalized Heisenberg algebras, SUSYQM and degeneracies: Infinite well and Morse potential. Workshop on Supersymmetric Quantum Mechanics and Spectral Design, Benasque, Spain, 18-30 July 2010. Kyiv, Ukraine: Natsional'na Akademiya Nauk Ukrainy. doi: 10.3842/SIGMA.2011.024

Polynomial associative algebras for quantum superintegrable systems with a third order integral of motion

Marquette, Ian (2008). Polynomial associative algebras for quantum superintegrable systems with a third order integral of motion. Institute for Mathematics and its Applications: Summer Program 2006, Minneapolis, MN, U.S.A., 17 July-4 August, 2006. New York, NY, United States: Springer New York. doi: 10.1007/978-0-387-73831-4_24