ao. Univ.-Prof. i.R. Dr. Thomas Hoffmann-Ostenhof

University of Vienna
Institute of Theoretical Chemistry
Währinger Str. 17
1090 Vienna
Austria

thoffmann(at)tbi.univie.ac.at
+43 1 4277 52768

Focus Area
Elliptic partial differential equations (like the time-independent Schroedinger equation) in relation to quantum mechanics and geometry. In particular, question related to regularity of solutions and spectral problems are considered.

The german Wikipedia also has an entry on Thomas Hoffmann-Ostenhof.

Publications
  1. On the choice of the zero-order operator in perturbation theory,
    with F. Mark, Chem. Phys. Lett. 17, 303-305 (1972)

  2. Variational bounds to overlap, with M. Hoffmann-Ostenhof, Chem.
    Phys. Lett. 31, 277-280 (1975)

  3. Lower bounds to the overlap, with M. Hoffmann-Ostenhof, G. Olbrich,
    J. Phys. A9, 27-33 (1976)

  4. Eine Ungleichung für die Funktionswerte einer samt ihrer Abbleitung
    quadratintegrablen Funktion, with M. Hoffmann-Ostenhof, Anzeiger d. Österr.
    Akad. d. Wiss. 8, 91-95 (1976)

  5. Exponentially decreasing upper bounds to the electron density of
    atoms, with M. Hoffmann-Ostenhof, Phys. Lett. 59A, 373-374 (1976)

  6. “Schrödinger inequalities” and asymptotic behavior of the electron
    density of atoms and molecules, with M. Hoffmann-Ostenhof, Phys. Rev.
    A16, 1782-1785 (1977)

  7. Bounds to expectation values and exponentially decreasing upper bounds
    to the one-electron density of atoms, with M. Hoffmann-Ostenhof, J. Phys.
    B11, 17-24 (1978)

  8. Simple bounds to the atomic one-electron density at the nucleus and to
    expectation values of one-electron operators, with M. Hoffmann-Ostenhof,
    W. Thirring, J. Phys. B11, L571-L575 (1978)

  9. Bounds for the long-range behavior of electronic wave functions, with
    R. Ahlrichs, M. Hoffmann-Ostenhof, J. Chem. Phys. 68, 1402-1410
    (1978)

  10. “Schrödinger inequalities” and asymptotic behavior of
    many-electron densities of atoms and molecules, with M. Hoffmann-Ostenhof,
    R. Ahlrichs, Phys. Rev. A18, 328-334 (1978)

  11. Lower and upper bounds to the decay of the ground state one-electron
    density of Helium-like systems, J. Phys. A12, 1181-1887 (1979)

  12. On the nodal structure of atomic eigenfunctions, with M.
    Hoffmann-Ostenhof, B. Simon, J. Phys. A13, 1131 – 1133 (1980)

  13. A comparison theorem for differential inequalities with applications
    in quantum mechanics, J. Phys A13, 417-424 (1980)

  14. A lower bound to the decay of ground states of two-electron atoms,
    Phys. Lett. 77A, 140-142 (1980)

  15. Brownian motion and a consequence of Harnack’s inequality: nodes
    of quantum wave functions, with M. Hoffmann-Ostenhof, B. Simon, Proc.
    Am. Math. Soc. 80, 301-305 (1980)

  16. On the exponential fall off of wave functions and electron densities,
    with M. Hoffmann-Ostenhof, R. Ahlrichs, J. D. Morgan III, LN in Physics 116,
    p. 62-67, Springer 1980

  17. Asymptotics of atomic ground states: the relation between the
    groundstate of helium and the ground state of He+, with J. M. Combes,
    M. Hoffmann-Ostenhof, J. Math. Phys. 22, 1299-1305 (1981)

  18. Bounds on the decay of electron densities with screening, with
    R. Ahlrichs, M. Hoffmann-Ostenhof, J. D. Morgan III, Phys. Rev. A23,
    2106-2117 (1981)

  19. The qualitative behavior of the ground state wave function of H2+,
    with J. Morgan III, J. Chem. Phys. 75, 843-846 (1981)

  20. L2-exponential lower bounds to solutions of the Schrödinger
    equations, with R. Froese, I. Herbst and M. Hoffmann-Ostenhof,
    Commun. Math. Phys. 87,
    265-286 (1982)

  21. On the absence of positive eigenvalues for one-body Schrödinger
    operators, with R. Froese, I. Herbst, M. Hoffmann-Ostenhof, J. d’Anal.
    41, 272-284 (1982)

  22. A multiparticle Coulomb system with bound state at threshold, with
    M. Hoffmann-Ostenhof, B. Simon, J. Phys. A16, 1125-1131 (1983)

  23. L2-lower bounds to solutions of one-body Schrödinger equations,
    with R. Froese, I. Herbst, M. Hoffmann-Ostenhof, Proc. Roy. Soc. Edinburgh
    95A, 2-38 (1983)

  24. On embedded eigenvalues for the one-dimensional Schrödinger equation,
    with M. Hoffmann-Ostenhof, J. Math. Phys. 25(8), 2490-2493 (1984)

  25. Absence of an L2-eigenfunction at the bottom of the spectrum
    of the Hamiltonian of the Hydrogen negative ion in the triplet S-sector,
    with M. Hoffmann-Ostenhof, J. Phys. A17, 3321-3325 (1984)

  26. Pointwise bounds on the asymptotics of spherically averaged
    L2-solutions of one-body Schrödinger operators, with M. Hoffmann-Ostenhof,
    J. Swetina, Ann. Inst. H. Poincaré, Sec. A42, 341-361 (1985)

  27. Continuity and nodal properties near infinity for solutions of
    2-dimensional Schrödinger equations, with M. Hoffmann-Ostenhof, J. Swetina,
    Duke Math. J. 53, 271-306 (1986)

  28. Asymptotics and continuity properties near infinity of solutions of
    Schrödinger equations in exterior domains, with M. Hoffmann-Ostenhof,
    J. Swetina, Ann. Inst. H. Poincaré, sec. A46 247 – 280 (1987)

  29. On the asymptotics of nodes of L2-solutions of Schrödinger
    equations in dimensions ≥ 3, with T. Hoffmann-Ostenhof, Commun. Math. Phys.
    117 49-77 (1988)

  30. Asymptotics properties of nodes of solutions to Schrödinger equations,
    with M. Hoffmann-Ostenhof, Symposium “Partial Differential Equations”,
    Holzhau (GDR) 1988, Teubner Texte zur Mathematik, Bd. 112, 157-162,
    Teubner, Leipzig 1989

  31. On the local behaviour of nodes of solutions of
    Schrödinger equations in dimensions ≥ 3, with M.
    Hoffmann-Ostenhof, Commun. PDE 15 (4), 435-451 (1990)

  32. On nodes of local solutions to Schrödinger equations,
    with M. Hoffman-Ostenhof, LN in Pure and Appl. Math., Vol. 133,
    Differential Equations with applications in biology, physics and
    engineering, Marcel Dekker, Inc., 201-208 (1991)

  33. Bounds on the order of vanishing of eigenfunctions of
    Schrödinger operators, with M. Hoffmann-Ostenhof, “Rigorous Results
    in Quantum Dynamics”, ed. by J. Dittrich and P. Exner, World
    Scientific Publ. 37 – 40, (1991)

  34. Local properties of solutions of Schrödinger equations,
    with M. Hoffmann-Ostenhof, Commun. PDE 17, 491-522, (1992)

  35. Electronic wave functions near coalescence points, with M.
    Hoffmann-Ostenhof, H. Stremnitzer, Phys.Rev. Letters 68, 3857-3860 (1992)

  36. Local behaviour of Coulombic wavefunctions, with M.
    Hoffmann-Ostenhof, H. Stremnitzer, Commun. Math. Phys.
    163, 185-215, (1994)

  37. Regularity on the nodal sets of solutions to Schrödinger
    equations, with M. Hoffmann-Ostenhof, N. Nadirashvili,
    “Mathematical results in Quantum Mechanics”, Int. Conf. in Blossin
    (Germany) May 17-21, 1993, Ed. by M. Demuth et. al., p. 19 – 25,
    Operator Theory: Advances and Appl. Vol. 70, Birkhäuser, Basel 1994

  38. Interior Hölder estimates for solutions of Schrödinger
    equations and the regularity of nodal sets, with M. Hoffmann-Ostenhof,
    N. Nadirashvili, Journees “Equationes aux derivees partielles”,
    Saint-Jean-de-Monts 30\. Mai au 3. Juin 1994, XIII, 1-9,
    Groupement de Recherche CNRS n0 1151

  39. Interior Hölder estimates for solutions of Schrödinger
    equations and the regularity of nodal sets, with M. Hoffmann-Ostenhof,
    N. Nadirashvili, Commun. PDE 20, 1241 – 1273, (1995)

  40. On some properties of zero sets and critical sets of
    solutions to elliptic equations, with M. Hoffmann-Ostenhof ,N.
    Nadirashvili, Centre de Recherches Mathematiques, CRM Proceedings and
    Lecture Notes 12, (1997) 167-176

  41. Critical sets of smooth solutions to elliptic equations
    in dimension 3, with M. Hoffmann-Ostenhof, N. Nadirashvili,
    Indiana Univ. Math. J. 45, 15-37, (1996)

  42. The nodal line of the second eigenfunction of the
    Laplacian in R2 can be closed, with M. Hoffmann-Ostenhof, N.
    Nadirashvili, Duke Math. J., 90, 632-640, (1997)

  43. On the nodal line conjecture, with M. Hoffmann-Ostenhof,
    N. Nadirashvili, Contemp. Math. 217,33-48, (1998)

  44. Critical sets of smooth solutions to elliptic equations,
    with R. Hardt, M. Hoffmann-Ostenhof, N. Nadirashvili,
    J. Differential Geom. 51, 359-373, (1999)

  45. Nodal sets of groundstates of Schrödinger operators
    with zero magnetic field in non-simply connected domains,
    with B. Helffer, M. Hoffmann-Ostenhof and M. P. Owen,
    Comm. Math. Phys 202, 629-649, (1999)

  46. On the multiplicity of eigenvalues of the Laplacian on surfaces,
    with M. Hoffmann-Ostenhof, N. Nadirashvili,
    Ann. Global Ana. Geom. 17 43-48, (1999)

  47. Bounds on the multiplicity of eigenvalues for fixed membranes,
    with P. Michor, N. Nadirashvili,
    Geom. Funct. Anal. 9, 1169-1188, (1999)

  48. Nodal sets, multiplicity and superconductivity in non simply
    connected domains, with B. Helffer, M. Hoffmann-Ostenhof, M.P. Owen
    LN in Pysics 62, Springer (2000), 63-84

  49. Electron wave functions and densities for atoms,
    with M. Hoffmann-Ostenhof, T. Oestergaard Soerensen,
    Ann. Henri Poincare 2, 77-100, (2001)

  50. A geometric version of Hardy’s inequality,
    with M. Hoffmann-Ostenhof and A. Laptev,
    Journal Funct. Anal. 189, 539-548, (2002)

  51. Spectral theory for the dihedral group,
    with B. Helffer, M. Hoffmann-Ostenhof and N. Nadirashvili,
    Geom. Funct. Anal. 12, 989-1017, (2002)

  52. The electron density is smooth away from the nuclei,
    with S. Fournais, M. Hoffmann-Ostenhof, T. Oestergaard Soerensen,
    Comm. Math. Phys. 228, 401-415, (2002)

  53. On the regularity of the density of electronic wavefunctions,
    with Søren Fournais, Maria Hoffmann-Ostenhof, T. Østergaard Sørensen,
    Contemporary Math. 307, 143-148 , (2002)

  54. Periodic Schrödinger operators and Aharonov-Bohm Hamiltonians, with
    with B. Helffer and N. Nadirashvili, Mosc. Math. J. 3, 45-61, 2003

  55. Spectral theory for periodic Schrödinger operators with reflection symmetries,
    with B. Helffer, Comm. Math. Phys 242, 501-529, (2003)

  56. Analyticity of the density of electronic wavefunctions, with S. Fournais, M. Hoffmann-Ostenhof, T. Østergaard
    Sørensen, Ark. Math. 42, 87-106, 2004

  57. Nodal domains a la Courant, with A. Ancona and B. Helffer, Doc. Math. 9, 283-299, (2004)
  58. Sharp regularity results for Coulombic many-electron wave functions,
    with S. Fournais, M. Hoffmann-ostenhof, T. Østergaard Sørensen,
    Comm. Math. Phys. 255, 183-227, (2005)

  59. Non-isotropic cusp conditions and regularity of the electron density of molecules at the nuclei,
    with S. Fournais, M. Hoffmann-ostenhof, T. Ø estergaard Sørensen,
    Ann Henri Poincaré 8, 731-748, (2007)

  60. Review of the book: the mathematics of the Bose gas and its condensation, by Elliott Lieb,
    Robert Seiringer, Janm Philip Solovej, Jakob Yngvason, Bull. Am. Math. Soc. 44, 493-496,(2007)

  61. Converse spectral problems for nodal domains, with B. Helffer, Mosc. Math. J. 7, 67-64, (2007)
  62. Positivity of the spherically averaged atomic one-electron density, with Søren Fournais,
    Maria Hoffmann-Ostenhof, Thomas Østergaard Sørensen, Math. Z. 259, 123-130, (2008)

  63. Many-particle Hardy inequalities, with Maria Hoffmann-Ostenhof, Ari Laptev and Jeper Tidblom,
    J. London Math. Soc. 77, 99-114, 2008

  64. Local and global properties of eigenfunctions and one-electron densities of Coulombic Schrödinger operators,
    with Søren Fournais, Maria Hoffmann-Ostenhof, Thomas Østergaard Sørensen,
    Jacob S. Møller (ed) et al, Quantum few-body systems. Proceedings of the joint physics/
    mathematics workshop on quantum
    few-body systems, Aarhus, Denmark 19-20 March 2007, Melville, NY: American Institue of Physics (AIP),
    AIP Conference Proceedings 998, 70-84, (2008)

  65. Aharonov-Bohm Hamiltonians, isospectrality and minimal partitions,
    with Virginie Bonnaillie-Noel, Bernard Hellfer, J. Phys. A, 42, 185203, (2009)

  66. Nodal domains and spectral minimal partitions,
    with Bernard Helffer and Susanna Terracini, Ann. Inst. Henri Poicaré, Anal. NonLinéaire 26,
    101-138, (2009)

  67. Analytic structure of many-body Coulombic wave functions,
    with Søren Fournais, Maria Hoffmann-Ostenhof, Thomas Østergaard Sørensen,
    Commun. Math. Phys. 289, 201-310, (2009)

  68. Analytic structure of solutions to multiconfigutration equations
    with Sørene Fournais, Maria Hoffmann-Ostenhof and Thomas Østergaard Sørensen,
    J. Phys. A. 42, 315208, (2009)

  69. On spectral minimal partitions: the case of the sphere
    with Bernard Helffer, Susanna Terracini,
    Ari Laptev (editor), Around the the research of Vladimir Maz’y III, Analysis and applications, Dordrecht: Springer; Novosibirs:
    Tamara Rozhkovskaya, Publisher: International Mathematical Series (New York) 13, 153-178, (2010)

  70. Nodal minimal partitions in dimension 3: with Bernard Helffer, Susanna Terracini,
    Discrete Contin. Dyn. Syst.28, 617-635, (2010)

  71. Remarks on two notions of spectral minimal partitions: with Bernard Helffer,
    Adv. Math. Sci. Appl. 20, (2010), 249-263

  72. Spectral minimal partitions for a thin strip on a cylinder or a thin annulus like domain with Neuann condition:
    with Bernard Helffer, Operator methods in mathematical physics, 107-115, Oper. Theory. Ad. Appl. 227,
    Birkhäuser/Springer Basel, (2010)

  73. On a magnetic characterization of spectral minimal partitions: with Bernard Helffer, J. Eur. Math. Soc. (JEMS),
    15, 2081-2092, (2013)

  74. Minimal partitions for anisotropic tori: with Bernard Helffer, to appear in J. Spectral Theory (2014).
  75. Eigenfunctions of 2-Dimensional Tori and for Rectangles with Neumann Boundary Conditions, Moscow Math J., 15, 101-106 (2015).
  76. Hardy inequalities with homogeneous weights: with A. Laptev, J. Funct. Anal., 268, 3278-3289 (2015).
  77. A review on large k minimal k-partitions and Pleijel’s Theorem: with B. Helffer, Contemporary Math. 640, Spectral Theory and Partial Differential equations . G. Eskin, L. Friedlander, J. Garnett, Editors. AMS 2015, 39-58 (2015).