prof. dr hab. Radosław Szmytkowski
Atomic Physics Division
Department of Atomic, Molecular and Optical Physics
Faculty of Applied Physics and Mathematics
Gdańsk University of Technology
ul. Narutowicza 11/12
PL 80-233 Gdańsk
Poland
e-mail: radek[at]mif.pg.gda.pl
tel.: +48-58-3472312
fax: +48-58-3472821

RESEARCH AREAS


PUBLICATIONS, E-PRINTS AND PREPRINTS

Publications may be downloaded for personal use only. Any other use requires prior permission of the author(s) and copyright owners.


BOOK

R. Szmytkowski
Metoda R-macierzy dla równań Schrödingera i Diraca
[R-matrix Method for the Schrödinger and Dirac Equations] (in Polish)
(Wydawnictwo Politechniki Gdańskiej, Gdańsk, 1999)
ISBN 83-88007-03-3 [preprint: PS | PDF]
(Original printed version of this book is available from the author, free of charge, upon request.)


JOURNAL PAPERS, CONFERENCE PAPERS, E-PRINTS AND PREPRINTS (reverse chronological order)



    2014

  1. R. Szmytkowski, S. Bielski
    A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices
    Integral Transforms Spec. Funct. 25 (2014) 312-7 [PDF]
  2. R. Szmytkowski, P. Stefańska
    Electric-field-induced magnetic quadrupole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
    Phys. Rev. A 89 (2014) 012501/1-7 [PDF]


  3. 2013

  4. R. Szmytkowski
    The parameter derivatives [2Pν(z)/∂ν2]ν=0 and [3Pν(z)/∂ν3]ν=0, where Pν(z) is the Legendre function of the first kind
    arXiv:1301.6586v1 [PDF]
  5. R. Szmytkowski
    Erratum to "Formulas and Theorems for the Special Functions of Mathematical Physics" by W. Magnus, F. Oberhettinger, R. P. Soni
    Math. Comput. 82 (2013) 1709-10


  6. 2012

  7. R. Szmytkowski
    Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)
    Integral Transforms Spec. Funct. 23 (2012) 847-52 [PDF]
    arXiv:1107.2680v2 [PDF]
  8. R. Szmytkowski
    Alternative approach to the solution of the momentum-space Schrödinger equation for bound states of the N-dimensional Coulomb problem
    Ann. Phys. (Berlin) 524 (2012) 345-52 [PDF]
  9. R. Szmytkowski, P. Stefańska
    Magnetic-field-induced electric quadrupole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
    Phys. Rev. A 85 (2012) 042502/1-6 [PDF]
  10. P. Stefańska, R. Szmytkowski
    Electric and magnetic dipole shielding constants for the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
    Int. J. Quantum Chem. 112 (2012) 1363-72 [PDF]
  11. R. Szmytkowski
    On parameter derivatives of the associated Legendre function of the first kind (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
    J. Math. Anal. Appl. 386 (2012) 332-42 [PDF]


  12. 2011

  13. R. Szmytkowski
    Alternative construction of the closed form of the Green's function for the wavized Maxwell fish-eye problem
    arXiv:1107.1768v1 [PDF]
  14. R. Szmytkowski, P. Stefańska
    Comment on "Four-component relativistic theory for NMR parameters: Unified formulation and numerical assessment of different approaches" [J. Chem. Phys. 130, 144102 (2009)]
    arXiv:1102.1811v1 [PDF]
  15. R. Szmytkowski
    On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
    J. Math. Chem. 49 (2011) 1436-77 [PDF]
    arXiv:0907.3217v1 [PDF]
  16. R. Szmytkowski
    Green's function for the wavized Maxwell fish-eye problem
    J. Phys. A: Math. Theor. 44 (2011) 065203/1-14 [PDF]
    arXiv:1107.1466v1 [PDF]


  17. 2010

  18. R. Szmytkowski
    A Hartree-Fock approach to the Steklov eigenproblem for a two-electron atom in an s2 state
    Theor. Chem. Acc. 127 (2010) 231-5 [PDF]
  19. R. Szmytkowski, S. Bielski
    An orthogonality relation for the Whittaker functions of the second kind of imaginary order
    Integral Transforms Spec. Funct. 21 (2010) 739-44 [PDF]
    arXiv:0910.1492v2 [PDF]
  20. R. Szmytkowski, S. Bielski
    Comment on the orthogonality of the Macdonald functions of imaginary order
    J. Math. Anal. Appl. 365 (2010) 195-7 [PDF]
    arXiv:0909.4232v1 [PDF]


  21. 2009

  22. R. Szmytkowski
    Some differentiation formulas for Legendre polynomials
    arXiv:0910.4715v1 [PDF]
  23. R. Szmytkowski
    A note on parameter derivatives of classical orthogonal polynomials
    arXiv:0901.2639v3 [PDF]
  24. R. Szmytkowski
    On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
    J. Math. Chem. 46 (2009) 231-60 [PDF]


  25. 2007

  26. R. Szmytkowski
    Addendum to 'On the derivative of the Legendre function of the first kind with respect to its degree'
    J. Phys. A: Math. Theor. 40 (2007) 14887-91 [PDF]
  27. R. Szmytkowski
    Recurrence and differential relations for spherical spinors
    J. Math. Chem. 42 (2007) 397-413 [PDF]
    arXiv:1011.3433v1 [PDF]
  28. R. Szmytkowski
    Closed forms of the Green's function and the generalized Green's function for the Helmholtz operator on the N-dimensional unit sphere
    J. Phys. A: Math. Theor. 40 (2007) 995-1009 [PDF]


  29. 2006

  30. R. Szmytkowski
    On the derivative of the Legendre function of the first kind with respect to its degree
    J. Phys. A: Math. Gen. 39 (2006) 15147-72 [PDF]
    Corrigendum: J. Phys. A: Math. Theor. 40 (2007) 7819-20 [PDF]
  31. R. Szmytkowski
    Closed form of the generalized Green's function for the Helmholtz operator on the two-dimensional unit sphere
    J. Math. Phys. 47 (2006) 063506/1-11 [PDF]
  32. S. Bielski, R. Szmytkowski
    Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Dirac equation
    J. Phys. A: Math. Gen. 39 (2006) 7359-81 [PDF]
  33. K. Mielewczyk, R. Szmytkowski
    Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
    Phys. Rev. A 73 (2006) 022511/1-11 [PDF]
    Erratum: Phys. Rev. A 73 (2006) 039908 [PDF]
  34. R. Szmytkowski
    Reply to "Comment on `Zero-range potentials for Dirac particles: Scattering and related continuum problems'"
    Phys. Rev. A 73 (2006) 026702/1-5 [PDF]
  35. R. Szmytkowski
    Relationship betwen the static dipole polarizability and the static dipole magnetizability of the relativistic hydrogenlike atom
    Chem. Phys. Lett. 419 (2006) 537-9 [PDF]
    Erratum: [PDF]


  36. 2005

  37. R. Szmytkowski
    Some summation formulae for spherical spinors
    J. Phys. A: Math. Gen. 38 (2005) 8993-9005 [PDF]
  38. R. Szmytkowski
    Zero-range potentials for Dirac particles: Scattering and related continuum problems
    Phys. Rev. A 71 (2005) 052708/1-19 [PDF]
  39. R. Szmytkowski, M. Gruchowski
    Ingoing and outgoing waves in the non-relativistic theory of photoionization
    J. Quant. Spectrosc. Radiat. Transfer 94 (2005) 127-36 [PDF]


  40. 2004

  41. R. Szmytkowski, M. Gruchowski
    Eigenchannel method for nonrelativistic scattering from zero-range potentials
    Phys. Rev. A 70 (2004) 062719/1-10 [PDF]
  42. R. Szmytkowski, S. Bielski
    Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Schrödinger equation
    Phys. Rev. A 70 (2004) 042103/1-12 [PDF]
  43. R. Szmytkowski, K. Mielewczyk
    Gordon decomposition of the static dipole polarizability of the relativistic hydrogen-like atom: application of the Sturmian expansion of the first-order Dirac-Coulomb Green function
    J. Phys. B: At. Mol. Opt. Phys. 37 (2004) 3961-72 [PDF]
  44. M. Gruchowski, R. Szmytkowski
    The finite-volume Dirac-Hartree-Fock method for confined relativistic many-electron systems
    J. Phys. A: Math. Gen. 37 (2004) 7783-98 [PDF]
  45. R. Szmytkowski, K. Mielewczyk
    Exact analytical scattering lengths for a class of long-range potentials with r - 4 asymptotics
    Phys. Rev. A 69 (2004) 064701/1-4 [PDF]
  46. R. Szmytkowski
    Eigenchannel method in quantum potential scattering
    Ann. Phys. (N.Y.) 311 (2004) 503-40 [PDF]
    Erratum: [PDF]
  47. R. Szmytkowski, S. Bielski
    Variational principles for bound states of Schrödinger and Dirac equations allowing the use of discontinuous trial functions
    Int. J. Quantum Chem. 97 (2004) 966-76 [PDF]
  48. R. Szmytkowski
    Fizyka na politechnice w Gdańsku w latach 1904-45
    [Physics at the technical university in Gdańsk in the years 1904-45] (in Polish)
    Pismo PG 12 (4) (2004) 11-3 [PDF]


  49. 2003

  50. R. Szmytkowski
    Derivation of Schwinger variational principles
    Phys. Lett. A 319 (2003) 233-9 [PDF]
  51. M. Gruchowski, R. Szmytkowski
    Relativistic theory of photoionization of one-electron systems: an eigenchannel R-matrix approach
    Radiat. Phys. Chem. 68 (2003) 143-6 [PDF]


  52. 2002

  53. R. Szmytkowski
    Magnetizability of the relativistic hydrogen-like atom: application of the Sturmian expansion of the first-order Dirac-Coulomb Green function
    J. Phys. B: At. Mol. Opt. Phys. 35 (2002) 1379-91 [PDF]
  54. R. Szmytkowski
    Larmor diamagnetism and Van Vleck paramagnetism in relativistic quantum theory: The Gordon decomposition approach
    Phys. Rev. A 65 (2002) 032112/1-8 [PDF]


  55. 2001

  56. R. Szmytkowski
    Dynamic polarizability of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the Dirac-Coulomb Green function
    Phys. Rev. A 65 (2001) 012503/1-8 [PDF]
  57. R. Szmytkowski
    Discontinuities in Dirac eigenfunction expansions
    J. Math. Phys. 42 (2001) 4606-17 [PDF]
  58. R. Szmytkowski, M. Gruchowski
    Completeness of the Dirac oscillator eigenfunctions
    J. Phys. A: Math. Gen. 34 (2001) 4991-7 [PDF]
  59. R. Szmytkowski
    Analogs of the Hellmann-Feynman theorem in the R-matrix theory
    Phys. Lett. A 280 (2001) 105-13 [PDF]
  60. R. Szmytkowski
    Variational R-matrix methods for many-electron systems: Unified relativistic theory
    Phys. Rev. A 63 (2001) 062704/1-14 [PDF]


  61. 2000

  62. R. Szmytkowski, B. Żywicka-Możejko
    Sturmian basis functions for the harmonic oscillator
    Phys. Rev. A 62 (2000) 022104/1-6 [PDF]
  63. R. Szmytkowski
    Remarks on completeness of many-electron Sturmians
    J. Phys. A: Math. Gen. 33 (2000) 4553-9 [PDF]
  64. R. Szmytkowski
    Variational R-matrix methods for many-electron systems: Unified nonrelativistic theory
    Phys. Rev. A 61 (2000) 022725/1-18 [PDF]
    Erratum: Phys. Rev. A 66 (2002) 029901 [PDF]
  65. R. Szmytkowski
    The Dirac-Coulomb Sturmians in the Z=0 limit: properties and applications to series expansions of the Dirac Green function and the Dirac plane wave
    J. Phys. A: Math. Gen. 33 (2000) 427-41 [PDF]


  66. 1999

  67. R. Szmytkowski
    Addendum to "The Dirac-Coulomb Sturmians and the series expansion of the Dirac-Coulomb Green function: application to the relativistic polarizability of the hydrogen-like atom" [J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 825-61, (E) 30 (1997) 2747]
    arXiv:physics/9902050v1 [PDF]
  68. R. Szmytkowski, Cz. Szmytkowski
    Scalar wave diffraction from zero-range scatterers
    J. Math. Chem. 26 (1999) 243-54 [PDF]


  69. 1998

  70. R. Szmytkowski
    Operator formulation of Wigner's R-matrix theories for the Schrödinger and Dirac equations
    J. Math. Phys. 39 (1998) 5231-52 [PDF]
    Erratum: J. Math. Phys. 40 (1999) 4181 [PDF]
  71. R. Szmytkowski
    Comment on "A simpler solution of the Dirac equation in a Coulomb potential," by B. Goodman and S. R. Ignjatović [Am. J. Phys. 65 (3), 214-221 (1997)]
    Am. J. Phys. 66 (1998) 635 [PDF]
  72. R. Szmytkowski
    Unified construction of variational R-matrix methods for the Dirac equation
    Phys. Rev. A 57 (1998) 4351-64 [PDF]
  73. R. Szmytkowski
    The continuum Schrödinger-Coulomb and Dirac-Coulomb Sturmian functions
    J. Phys. A: Math. Gen. 31 (1998) 4963-90 [PDF]
    Erratum: J. Phys. A: Math. Gen. 31 (1998) 7415-6 [PDF]
  74. R. Szmytkowski
    A generalization of Wigner's R-matrix method
    Phys. Lett. A 237 (1998) 319-30 [PDF]


  75. 1997

  76. R. Szmytkowski, Cz. Szmytkowski
    Quantum proximity resonances
    Phys. Lett. A 235 (1997) 217-21 [PDF]
  77. R. Szmytkowski
    A unified construction of variational R-matrix methods: I. The Schrödinger equation
    J. Phys. A: Math. Gen. 30 (1997) 4413-38 [PDF]
  78. R. Szmytkowski
    The Dirac-Coulomb Sturmians and the series expansion of the Dirac-Coulomb Green function: application to the relativistic polarizability of the hydrogen-like atom
    J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 825-61 [PDF]
    Erratum: J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 2747 [PDF]
    Addendum: arXiv:physics/9902050v1 [PDF]


  79. 1996

  80. R. Szmytkowski, J. Hinze
    Kapur-Peierls and Wigner R-matrix theories for the Dirac equation
    J. Phys. A: Math. Gen. 29 (1996) 6125-41 [PDF]
  81. R. Szmytkowski, J. Hinze
    Convergence of the non-relativistic and relativistic R-matrix expansions at the reaction volume boundary
    J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 761-77 [PDF]
    [Erratum: J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 3800-1 [HTML]]
  82. R. Szmytkowski
    Analytical independent-particle model for electron scattering by argon at low energy
    Few-Body Syst. 20 (1996) 175-80 [PDF]


  83. 1995

  84. R. Szmytkowski
    Analytical calculations of scattering lengths in atomic physics
    J. Phys. A: Math. Gen. 28 (1995) 7333-45 [PDF]
  85. R. Szmytkowski, Cz. Szmytkowski
    Collisions of fast electrons with positronium atoms
    Nuovo Cimento D 17 (1995) 1007-18 [PDF]
    [preprint: Cz. Szmytkowski, R. Szmytkowski
    Collisions of fast electrons with positronium atoms
    Zeszyty Naukowe Politechniki Gdańskiej Fizyka 30 (1994) 27-40]
  86. R. Szmytkowski
    The relativistic multi-channel variable phase method for solving asymptotic equations in electron-atom and electron-ion scattering
    Comput. Phys. Commun. 90 (1995) 244-50 [PDF]
  87. R. Szmytkowski, A. M. Alhasan
    Relativistic calculations of static electric polarizabilities for alkaline-earth-metals and their isoelectronic sequences
    Phys. Scr. 52 (1995) 309-12 [PDF]
  88. R. Szmytkowski
    Calculation of the electron-scattering lengths for rare-gas atoms
    Phys. Rev. A 51 (1995) 853-4 [PDF]


  89. 1994

  90. R. Szmytkowski, J. E. Sienkiewicz
    Elastic scattering of electrons by strontium and barium atoms
    Phys. Rev. A 50 (1994) 4007-12 [PDF]
  91. R. Szmytkowski
    Elastic positron scattering from krypton and xenon in the relativistic polarized orbital approximation
    Acta Phys. Pol. A 86 (1994) 309-14 [PDF]
  92. R. Szmytkowski, J. E. Sienkiewicz
    Spin polarization of slow electrons elastically scattered from xenon atoms
    J. Phys. B: At. Mol. Opt. Phys. 27 (1994) 2277-82 [PDF]
  93. R. Szmytkowski, J. E. Sienkiewicz
    Spin polarization of slow electrons elastically scattered from mercury, cadmium and zinc atoms
    J. Phys. B: At. Mol. Opt. Phys. 27 (1994) 555-63 [PDF]
  94. Cz. Szmytkowski, R. Szmytkowski
    On the contribution of higher partial waves to scattering by the long-range inverse power potentials
    Zeszyty Naukowe Politechniki Gdańskiej Fizyka 30 (1994) 19-25


  95. 1993

  96. R. Szmytkowski
    Elastic positron scattering from zinc and cadmium in the relativistic polarized orbital approximation
    Acta Phys. Pol. A 84 (1993) 1035-40 [PDF]
  97. R. Szmytkowski
    Theoretical study of low-energy positron scattering on alkaline-earth atoms in the relativistic polarized orbital approximation
    J. Phys. II (France) 3 (1993) 183-9 [PDF]
  98. R. Szmytkowski
    The elastic positron scattering from mercury in the relativistic polarized orbital method
    J. Phys. B: At. Mol. Opt. Phys. 26 (1993) 535-45 [PDF]
  99. R. Szmytkowski, A. M. Alhasan
    Relativistic polarized orbital calculations of polarizabilities for the alkaline-earth-metals and their isoelectronic sequences
    Bull. Fac. Sci. Assiut Univ. Phys. 22 (1993) 25-45


  100. 1992

  101. R. Szmytkowski
    Charged particle in the uniform static magnetic field: An operator solution to the classical problem
    Am. J. Phys. 60 (1992) 945 [PDF]
  102. R. Szmytkowski
    Obliczanie momentów bezwładności niektórych brył symetrycznych
    [Calculations of moments of inerta of some symmetric solids] (in Polish)
    Fizyka w Szkole 38 (5) (1992) 270-2


  103. 1991

  104. R. Szmytkowski
    The relativistic polarized orbital theory of the elastic electron and positron scattering from closed shell atoms
    J. Phys. B: At. Mol. Opt. Phys. 24 (1991) 3895-904 [PDF]
  105. R. Szmytkowski
    On the exact calculation of the scattering lengths for long range potentials II. Lenz potentials
    Acta Phys. Pol. A 79 (1991) 613-8 [PDF]


  106. 1990

  107. R. Szmytkowski
    On the exact calculation of the scattering lengths for long range potentials I. The inverse power potentials
    Acta Phys. Pol. A 78 (1990) 517-22
  108. R. Szmytkowski
    Calculation of the electron scattering lengths for noble atoms
    Fizika (Zagreb) 22 (1990) 481-7
  109. R. Szmytkowski
    Jak obliczyć momenty bezwładności bez całkowania
    [How to calculate moments of inertia without integration] (in Polish)
    Delta (11) (1990) 10-1


  110. 1988

  111. R. Szmytkowski
    Simple method of calculation of moments of inertia
    Am. J. Phys. 56 (1988) 754-6 [PDF]
  112. R. Szmytkowski
    Matrix elements of long-range potentials with Gaussian cut-off function over Cartesian Gaussian functions
    in: Proceedings of the 3rd International Conference for Physics Students, Prague, Czechoslovakia, 6-10 September 1988
    (International Association of Physics Students, Budapest, 1988), pp. 75-80


  113. 1987

  114. R. Szmytkowski
    Moment bezwładności w geometrii
    [Moment of inertia in geometry] (in Polish)
    Delta (1) (1987) 6-8

THESES SUPERVISED (reverse chronological order)


TEACHING (text in Polish)

UWAGA! Dodatkowe terminy z "Metod matematycznych fizyki II" (VI semestr Fizyki Stosowanej I):
Konsultacje w sesji letniej 2013/14:
Przedmioty prowadzone w semestrze letnim 2013/14: