- (with B. Roy) Rational extension and Jacobi-type X
_{m}solutions of a quantum nonlinear oscillator, J. Math. Phys. 54 (2013), 122104 (12pp) - (with J. Morris) An exactly-solvable three-dimensional nonlinear quantum oscillator, J. Math. Phys. 54 (2013), 112107 (17pp)
- Wronskian representation for confluent supersymmetric transformation chains of arbitrary order, Eur. Phys. J. Plus 128 (2013), 68 (17pp)
- (with J. Morris) Higher-dimensional realization of a nonlinear, one-parameter quantum oscillator, Eur. Phys. J. Plus 128 (2013), 54 (11pp)
- Darboux operators for linear first-order multi-component equations in arbitrary dimensions, Cent. Eur. J. Phys. 11 (2013), 457-469
- (with C. Gordon) Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions, J. Math. Phys. 54 (2013), 042108 (15pp)
- Comment on "Nonsingular parametric oscillators Darboux-related to the classical harmonic oscillator" by H.C. Rosu et al., Europhys. Lett. 101 (2013), 30001 (2pp)
- Darboux transformations for energy-dependent potentials and the Klein-Gordon equation, Math. Physics, Analysis and Geometry (2013), http://dx.doi.org/10.1007/s11040-012-9126-6
- (with J. Garcia-Ravelo, C. Pacheco-Garcia and J.J. Pena Gil) A position-dependent mass model for the Thomas-Fermi potential: exact solvability and relation to δ-doped semiconductors, Ann. Physics 333 (2013), 323–334
- (with J. Garcia-Ravelo and A. Trujillo) Explicit formulas for generalized harmonic perturbations of the infinite quantum well with an application to Mathieu equations, J. Math. Phys. 53 (2012), 102101 (14pp)
- Two-dimensional magnetic Schrödinger equations, Darboux transformations and solutions of associated auxiliary equations, J. Math. Phys. 53 (2012), 082108 (15pp)
- Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix, J. Math. Phys. 53 (2012), 103519 (11pp)
- (with J. Morris) Special function solutions of a spectral problem for a nonlinear quantum oscillator, J. Phys. A 45 (2012), 305301 (9pp)
- Higher-order Darboux transformations with foreign auxiliary equations and equivalence with generalized Darboux transformations, Appl. Math. Lett. 25 (2012), 1520–1527
- Combined Sundman-Darboux transformations and solutions of nonlinear ordinary differential equations of second order, Adv. Pure Appl. Math. 3 (2012), 165-180
- Explicit higher-dimensional Darboux transformations for the time-dependent Schrödinger equation, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, AMS Contemporary Mathematics series 563 (2012)
- Two-dimensional generalized harmonic oscillators and their Darboux partners, J. Phys. A 44 (2011), 495304 (20pp)
- Higher-order Darboux transformations in two dimensions, linearizable auxiliary equations and invariant potentials, J. Math. Phys. 52 (2011), 083505 (9pp)
- (with H. Cobian), Time-dependent Schrödinger equations with effective mass in (2+1) dimensions: intertwining relations and Darboux operators, J. Phys. A 44 (2011), 285301 (14pp)
- Modified Darboux transformations with foreign auxiliary equations, Phys. Lett. A 375 (2011), 2513-2518
- Two-dimensional Darboux transformations for non-separable angular equations and solvable non-central potentials, J. Math. Chem. 49 (2011), 1302-1310
- Quasi-exact solvability of a hyperbolic intermolecular potential induced by an effective mass step, Internat. J. Math. Math. Sci. 2011 (2011), article #358198 (9pp)
- Propagators of generalized Schrödinger equations related by first-order supersymmetry, Acta Polytechnica 51 (2011), 63-69
- (with E. Pozdeeva), Propagators of generalized Schrödinger equations related by higher-order supersymmetry, Internat. J. Modern Phys. A 26 (2011), 191-207
- (with E. Pozdeeva), Darboux transformations for a generalized Dirac equation in two dimensions, J. Math. Phys. 51 (2010), 113501 (15pp)
- (book chapter) Linear generalizations of the time-dependent Schrödinger equation: point transformations, Darboux transformations, and their properties, Quantum Mechanics, (Nova Science Publishers, New York, 2010)
- Exact quantization formula for affine linearly energy-dependent potentials, Cent. Eur. J. Phys. 9 (2010), 57-64
- Green's functions and trace formulas for generalized Sturm-Liouville problems related by Darboux transformations, J. Math. Phys. 51 (2010), 053501 (13pp)
- Intertwining relations and Darboux transformations for Schrödinger equations in (n+1) dimensions, J. Math. Phys. 51 (2010), 033521 (11 pp)
- (with J. Garcia-Ravelo, J. Pena and A. Queijeiro), Two-parameter ladder operators for spherical Bessel functions, Appl. Math. Lett. 23 (2010), 462-465
- (with J. Carballo Jimenez), Darboux transformations for the time-dependent nonhomogeneous Burgers equation in (1+1) dimensions, Phys. Scripta 80 (2009), 065014 (8pp)
- (with J. Carballo Jimenez), Supersymmetry of generalized linear Schrödinger equations in (1+1) dimensions, Symmetry 1 (2009), 115-144
- (with J. Garcia-Ravelo, J. Garcia Martinez and J. Pena), Exactly solvable energy dependent potentials, Phys. Lett. A 373 (2009), 3619-3623
- (with A. Suzko), Darboux transformations and supersymmetry for generalized Schrödinger equations in (1+1) dimensions, J. Phys. A 42 (2009), 295203 (14pp)
- (with E. Pozdeeva and A. Suzko), Explicit Darboux transformations of arbitrary order for generalized time-dependent Schrödinger equations, J. Phys. A 42 (2009), 115211 (12pp)
- (with J. Garcia-Ravelo, J. Morales, J. Pena and P. Roy), Exact solutions of the Fokker-Planck equation from an n-th order supersymmetric quantum mechanics approach, Phys. Lett. A 373 (2009), 1610-1615
- (with J. Garcia-Ravelo and J. Pena), An implicit spectral formula for generalized linear Schrödinger equations, Internat. J. Modern Phys. E 18 (2009), 1831-1844
- (with A. Suzko and E. Velicheva), Supersymmetry and Darboux transformations for the generalized Schrödinger equation, Physics of Atomic Nuclei 72 (2009), 858-865
- (with J. Pena and E. Zamora-Gallardo), Arbitrary-order Darboux transformations for position-dependent mass Schrödinger equations with noncentral potential, Int. J. Quant. Chem. 109 (2009), 1464-1471
- (with A. Suzko), Intertwining operator method and supersymmetry for effective mass Schrödinger equations, Phys. Lett. A 372 (2008), 5865-5871
- (with E. Pozdeeva), Trace formula for Dirac Green's functions related by Darboux transformations, J. Phys. A 41 (2008), 265201 (13pp)
- Generalized linear Schrödinger equations and their Darboux transformations, Cent. Eur. J. Phys. 6 (2008), 654-661
- (with E. Pozdeeva), Trace formula for Green's functions of effective mass Schrödinger equations and N-th order Darboux transformations, Internat. J. Modern Phys. A 23 (2008), 2635-2647
- Darboux transformations for effective mass Schrödinger equations with energy-dependent potentials, Internat. J. Modern Phys. A 23 (2008), 537-546
- Supersymmetry of time-dependent Schrödinger equations with effective mass, Cent. Eur. J. Phys. 6 (2008), 153-157
- Reduction of time-dependent Schrödinger equations with effective mass to stationary Schrödinger equations, Research Letters in Physics (2008), DOI:10.1155/2008/589269
- Darboux transformations for N-dimensional effective mass Schrödinger equations with hyperspherical symmetry, Internat. J. Modern Phys. A 22 (2007), 3293-3304
- Fractional Darboux transformations are point canonical transformations, Il Nuovo Cimento B 121 (2007), 1025-1028
- Form-preserving transformations for the time-dependent Schrödinger equation in (n+1) dimensions, Math. Physics, Analysis and Geometry 9 (2007), 371-388
- Fractional Darboux transformations for the time-dependent Schrödinger equation, International Journal of Pure and Applied Mathematics 37 (2007), 489-506
- New exact solutions of the non-homogeneous Burgers equation in (1+1) dimensions, Phys. Scr. 75 (2007), 531-536
- Effective mass Hamiltonians with linear terms in the momentum: Darboux transformations and form-preserving transformations, International J. Modern Phys. A 22 (2007), 1735-1769
- Form-preserving transformations of the time-dependent Klein-Gordon equation and the generation of solvable potentials, Phys. Scripta 74 (2006), 452-458
- Exactly solvable combinations of scalar and vector potentials for the Dirac equation interrelated by Riccati equations, Chinese Phys. Lett. 23 (2006), 1365-1368
- Reality condition for Darboux transformations of time-dependent Schrödinger equations with effective mass, Internat. J. Modern Phys. A 21 (2006), 4853-4868
- A simple method for constructing non-liouvillian .rst integrals of autonomous planar systems, Czechoslovak Math. J. 56 (2006), 987-999
- (with D. Stoffer and A. Aschwanden), Stable periodic solutions for delay equations with positive feedback - a computer-assisted proof, Discrete Contin. Dyn. Syst. 14 (2006), 721-736
- Darboux transformations for time-dependent Schrödinger equations with effective mass, Internat. J. Modern Phys. A 21 (2006), 1359-1377
- Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions, Cent. Eur. J. Phys. 3 (2005), 591-609
- Comment on: D.-Y. Song and J.R. Klauder, "Generalization of the Darboux transformation and generalized harmonic oscillators", J. Phys. A 36 (2003), no. 32, 8673-8684, J. Phys. A 38 (2005), 5831-5836
- Form-preserving transformations for Hamiltonians with linear terms in the momentum, Found. Phys. Lett. 18 (2005), 535-548.
- On quasi-exact solvability of the Schrödinger equation for a free particle on the surface of a spindle torus, Found. Phys. Lett. 18 (2005), 291-300
- Form-preserving transformations of the time-dependent Schrödinger equation with time and position-dependent mass, Commun. Theor. Phys. 43 (2005), 657-665
- Orbitally asymptotically stable periodic solutions of delay equations with positive feedback, Mitt. Math. Sem. Giessen 252 (2003), 1-106 and Mitt. Math. Sem. Giessen 254 (2004), 48-90
- Exact wavefunctions and energies of a non-relativistic free quantum particle on the surface of a degenerate torus, Modern Phys. Lett. A 19 (2004), 1759-1766
- Non-existence of liouvillian solutions for a free quantum particle on a torus surface, part 1: polar states, Found. Phys. Lett. 17 (2004), 677-690
- N-multiplets of the radial Dirac equation, Chinese J. Phys. 42 (2004), 234-242
- Quasi-exactly solvable potentials of the radial Dirac equation with two known levels, Chinese J. Phys. 42 (2004), 117-126
- A new formula to obtain exact Green's functions of the time-dependent Schrödinger equation, Commun. Theor. Phys. 41 (2004), 723-725
- Exact solutions of the time-dependent Schrödinger equation with time-dependent mass generated by functional and coordinate transformations, Hadronic J. 27 (2004), 485-498
- Functional transformation of the time-dependent Schrödinger equation with time- and spatially dependent mass, Hadronic J. 26 (2003), 707-714
- Equivalence of time-dependent Schrödinger equations with constant and time-dependent mass, Modern Phys. Lett. A 18 (2003), 2829-2835
- Hidden symmetry in quasi-exactly solvable fractional power potentials, Progr. Theoret. Phys. 110 (2003), 1235-1240
- (with S.K. Bose), Improved SUSY inspired variational method to obtain bound state energies of the screened Coulomb potential, Modern Phys. Lett. A 18 (2003), 853-857
- A method of generating exact solutions of the time-dependent Schrödinger equation with time-dependent mass, Modern Phys. Lett. A 17 (2002), 1567-1573
- Closed-form solutions of the Schrödinger equation for a particle on the torus, Found. Phys. Lett. 15 (2002), 585-589
- General solution of a system of di.erential equations modeling a class of exactly-solvable potentials, part 2: extended results, Proc. Estonian Acad. Sci. Phys. Math. 51 (2002), 179-193
- Quasi-exactly solvable singular fractional power potentials emerging from the triconfluent Heun equation, Phys. Scripta 65 (2002), 373-376
- A class of exact solutions of the time-dependent Schrödinger equation with time-dependent mass, Modern Phys. Lett. A 16 (2002), 2557-2566
- The central symmetric screened Coulomb potential in N dimensions, Hadronic J. 24 (2001), 519-530
- (with S.K. Bose and M. Singh), New exact solutions of the Dirac equation, Phys. Lett. A 287 (2001), 321-324
- Comment on Phys. Scripta 60, 195 (1999), Phys. Scripta 64 (2001), 96
- General solution of a system of di.erential equations modeling a class of exactly-solvable potentials, Proc. Estonian Acad. Sci. Phys. Math. 50 (2001), 42-48
- On normalizability of zero energy solutions of the Schrödinger equation, Hadronic J. 23 (2000), 683-687
- (with S.K. Bose), Exact solution of the Dirac equation for a singular central power potential, Modern Phys. Lett. A 15 (2000), 1583-1588
- Exact solutions of the Schrödinger equation with irregular singularity, Internat. J. Theoret. Phys. 39 (2000), 2305-2325
- (with S.K. Bose), Properties of an algebraic transformation for 1D Schrödinger potentials, Phys. Scripta 62 (2000), 241-247
- (with S.K. Bose), An interesting and useful transformation for the nonrelativistic Schrödinger equation, Hadronic J. 23 (2000), 249-257
- On finite normal series solutions of relativistic wave equations, Found. Phys. Lett. 13 (2000), 265-277
- On finite normal series solutions of the Schrödinger equation with irregular singularity, Found. Phys. Lett. 13 (2000), 11-27
- Exact bound states for the symmetric screened Coulomb potential, Phys. Scripta 61 (2000), 641-645
- Exact algebraic bound states for the potential V (r) = k2/r2 + k3/r3 + k4/r4,
Hadronic J. 22 (1999), 343-350