Axel Schulze-Halberg
Department of Mathematics and Actuarial Science
Assistant Professor
At IU Northwest since 2009
SCHOLARLY PUBLICATIONS AND CREATIVE ACHIEVEMENTS
ARTICLES (in refereed journals):
(with J. Carballo Jimenez). "Supersymmetry of generalized linear Schrödinger equations in (1+1) dimensions." Forthcoming in Symmetry (2009).
(with J. Garcia-Ravelo and J. Pena). "An implicit spectral formula for generalized linear Schrödinger equations." Forthcoming in International J. Modern Phys. E (2009).
(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 the generalized Schrödinger equations in (1+1) dimensions." J. Phys. A 42 (2009), 295203-295217.
(with E. Pozdeeva and A. Suzko). "Explicit Darboux transformations of arbitrary order for generalized time-dependent Schrödinger equations." J. Phys. A 42 (2009), 115211-115223
(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 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.