Publications and Preprints

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Papers

• (with S. Fournais)
  Estimates on derivatives of Coulombic wave functions and their electron densities.
  J. reine angew. Math. 775 (2021), 1–38.

  [ zbMATH:  Zbl 07355559  ]  [ MathReviews:  MR4265183 ]  [ arXiv:  arXiv:1803.03495 ]

• (with S. Fournais, J. Lampart, and M. Lewin)
  Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory.
  Phys. Rev. A 93, 062510 (2016).

  [ arXiv:  arXiv:1603.02219 ]

• (with A. Dall'Acqua, S. Fournais, and E. Stockmeyer)
  Real analyticity of solutions to Schrödinger equations involving a fractional Laplacian and other Fourier multipliers.
  XVIIth International Congress on Mathematical Physics (2013), 600–609
  (Proceedings of ICMP12, Aalborg, Denmark, August 6–11, 2012).

  [ zbMATH:  Zbl 1302.81092  ]  [ MathReviews:  MR3204512 ]  [ arXiv:  arXiv:1209.3885v2 ]

• (with A. Dall'Acqua, S. Fournais, and E. Stockmeyer)
  Real analyticity away from the nucleus of pseudorelativistic Hartree-Fock orbitals.
  Analysis & PDE 5 (2012), no. 3, 657–691.

  [ zbMATH:  Zbl 1267.35174  ]  [ MathReviews:  MR2994509 ]   [ arXiv:  arXiv:1103.5026v2 ]

• (with S. Fournais)
  The Electron Densities of Pseudorelativistic Eigenfunctions are Smooth Away from the Nuclei.
  Comm. Partial Differential Equations 35 (2010), no. 7, 1276–1291.

  [ zbMATH:  Zbl 1205.35240  ]  [ MathReviews:  MR2753635 ]   [ arXiv:  arXiv:0811.4537v1 ]

• (with J.P. Solovej and W.L. Spitzer)
  Relativistic Scott correction for atoms and molecules.
  Comm. Pure Appl. Math. 63 (2010), no. 1, 39–118.

  [ zbMATH:  Zbl 1182.81065  ]  [ MathReviews:  MR2588386  ]  [ arXiv:  arXiv:0808.2163v1 ]

• (with S. Fournais, M. and T. Hoffmann-Ostenhof)
  Analytic structure of solutions to multiconfiguration equations.
  J. Phys. A: Math. Theor. 42 (2009) 315208.

  [ zbMATH:  Zbl 1181.35282  ]  [ MathReviews:  MR2521310 ]  [ arXiv:  arXiv:0812.1429v1 ]

• (with S. Fournais, M. and T. Hoffmann-Ostenhof)
  Analytic Structure of Many-Body Coulombic Wave Functions.
  Commun. Math. Phys. 289 (2009), no. 1, 291–310

  [ zbMATH:  Zbl 1171.35110  ]  [ MathReviews:  MR2504851 ]  [ arXiv:  arXiv:0806.1004v1 ]

• (with S. Fournais and M. Hoffmann-Ostenhof)
  Third Derivative of the One-Electron Density at the Nucleus.
  Ann. Henri Poincaré 9 (2008), no. 7, 1387–1412.

  [ zbMATH:  Zbl 1160.81028  ]  [ MathReviews:  MR2453253 ]  [ arXiv:  math-ph/0607004 ]

• (with A. Dall'Acqua and E. Stockmeyer)
  Hartree-Fock Theory for Pseudorelativistic Atoms,
  Ann. Henri Poincaré 9 (2008), no. 4, 711–742.
  

  [ zbMATH:  Zbl 1192.81406  ]  [ MathReviews:  MR2413201 ]  [ arXiv:  0707.4612v1[math-ph] ]

• (with S. Fournais, M. and T. Hoffmann-Ostenhof)
  Local and global properties of eigenfunctions and one-electron densities of Coulombic Schrödinger operators,
  AIP Conference Proceedings volume 998 (2008):
  'Quantum Few-Body Systems', Aarhus, Denmark, 19–20 March 2007.

  [ zbMATH:  Zbl 1180.81057  ]

•             , Positivity of the spherically averaged atomic one-electron density,
  Math. Z. 259 (2008) no. 1, 123–130.

  [ zbMATH:  Zbl 1138.81567  ]  [ MathReviews:  MR2375619 ]  

• (with E. Stockmeyer)
  On the convergence of eigenfunctions to threshold energy states,
  Proc. R. Soc. Edinb., Sect. A, Math. 138A (2008), 169–187.

  [ zbMATH:  Zbl 1146.35063  ]  [ MathReviews:  MR2388942 ]  [ arXiv:  math-ph/0604015 ]

• (with S. Fournais, M. and T. Hoffmann-Ostenhof)
  Non-Isotropic Cusp Conditions and Regularity of the Electron Density of Molecules at the Nuclei,
  Ann. Henri Poincaré 8 (2007), no. 4, 731–748.
  

  [ zbMATH:  Zbl 1126.81054  ]  [ MathReviews:  MR2333780 ]  [ arXiv:   math-ph/0603019 ]

• The large-Z Behaviour of pseudorelativistic atoms,
  J. Math. Phys., 46, 052307 (2005).

  [ zbMATH:  Zbl 1110.81162  ]  [ MathReviews:  MR2142995 ]  [ arXiv:  math-ph/0408056 ]

• (with S. Fournais, M. and T. Hoffmann-Ostenhof)
  Sharp Regularity Results for Coulombic Many-Electron Wave Functions,
  Commun. Math. Phys. 255 (2005), no. 1, 183–227

  [ zbMATH:  Zbl 1075.35063  ]  [ MathReviews:  MR2123381 ]  [ arXiv:  math-ph/0312060 ]

•             , Analyticity of the density of electronic wavefunctions,
  Ark. Mat. 42 (2004), 87–106.
  

  [ zbMATH:  Zbl 1068.35118  ]  [ MathReviews:  MR2056546 ]  [ arXiv  math-ph/0211075 ]

•             , On the regularity of the density of electronic wavefunctions.,
  In 'Mathematical results in quantum mechanics (Taxco, 2001)', 143--148,
  Contemp. Math., 307, Amer. Math. Soc., Providence, RI, 2002.
  

  [ zbMATH:  Zbl 1041.81104  ]  [ MathReviews:  MR1946025  ]  [ arXiv:  math-ph/0211070 ]

•             , The Electron Density is Smooth Away from the Nuclei,
  Commun. Math. Phys. 228 (2002), no. 3, 401–415.
  

  [ zbMATH:  Zbl 1005.81095  ]  [ MathReviews:  MR1918782  ]  [ arXiv:  math-ph/0109020 ]

• (with M. and T. Hoffmann-Ostenhof)
  Electron Wavefunctions and Densities for Atoms,
  Ann. Henri Poincaré 2 (2001), no. 1, 77–100.
  

  [ zbMATH:  Zbl 0985.81133 ]  [ MathReviews:  MR1823834 ]  [ arXiv:  math.AP/0005018 ]

Theses

• Non-relativistic and pseudorelativistic quantum mechanics of atoms and molecules,
  Habilitation thesis, Department of Mathematics, LMU Munich, Germany, 2009.
  
• Towards a Relativistic Scott Correction,
  Ph.D. thesis, Department of Mathematical Sciences, University of Aarhus, Denmark, 1998.
• The Large-Z Behaviour of Pseudo-Relativistic Atoms,
  Progress-report, Department of Mathematical Sciences, University of Aarhus, Denmark, 1996.