Mathematical Methods of Quantum Mechanics

Research topics

We apply geometric, functional-analytic, algebraic, and operator-theoretic methods to the study of models and problems of relevance for quantum mechanics, mainly arising from solid state physics and and theoretical physics.
  • Many-body quantum dynamics and effective non-linear Schrödinger equations
  • Multi-scale methods and emergent effects in quantum systems
  • Well-posedness, dispersive, and scattering properties of non-linear PDEs for quantum dynamics (NLS, Hartree, Schrödinger-Maxwell, non-linear delta)
  • Self-adjoint extensions techniques and application to quantum models
  • Quantum systems with zero-range interactions
  • Quantum particles constrained on graphs and surfaces
  • Models for quantum decoherence
  • Topological and geometric effects in solid state physics
  • C*-algebraic quantum statistical mechanics

Principal Investigators

Research Students

Main External Collaborators

Local Activities

Joint projects

  • COND-MATH 2014-2017
    FIR-MIUR grant "Condensed Matter in Mathematical Physics"
  • CAS-LMU 2013-2014
    Research in Residence at the Centre for Advanced Studies at LMU Munich
  • NANOMATH 2006-2007
    INdAM project "Mathematical Modeling and Numerical Analysis of Quantum Systems with Applications to Nanosciences"

Workshops and Conferences

    Scientific events co-organised by us, or participated by us as speakers.

  • ZR3-2018
    Workshop "Mathematical Challenges of Zero-Range Physics: rigorous results and open problems"
    Rome, 9-13 July 2018
  • MCQM-2018
    School and workshop "Mathematical challenges in quantum mechanics"
    Rome, 19-24 February 2018
  • TQMS-2018
    Conference "Trails in Quantum Mechanics and Surroundings"
    SISSA Trieste, 29-30 January 2018
  • Insubria-2017
    Conference "Insubria Summer School in Mathematical Physics"
    Como, 18-22 September 2017
  • HAST-PDE-2017
    Summer school and workshop "Harmonic Analysis, Spectral Theory, and PDEs"
    Rome, 12-15 September 2017
  • STDE-2017
    5th Najman conference on "Spectral Theory and Differential Equation"
    Opatija, 10-15 September 2017
  • Cortona-2017
    Summer School "Nonlinear dispersive PDE, quantum many-particle systems, and the world between"
    Cortona, 17-28 July 2017
  • CTMP-2017
    Summer School "Current topics in Mathematical Physics"
    Zurich, 17-21 July 2017
  • JTQD-2017
    Junior Symposium "The Junior Trieste Quantum Days 2017"
    SISSA, Trieste 12 and 19 May 2017
  • TSQD 2017
    Conference "Trieste Quantum Days 2017"
    SISSA, Trieste 20-24 February 2017
  • Dirac 2017
    Workshop "Linear and Nonlinear Dirac Equation: advances and open problems"
    Como, 8-10 February 2017
  • ZR2-2016
    Workshop "Mathematical Challenges of Zero-Range Physics: rigorous results and open problems"
    SISSA, 7-10 November 2016
  • SAMMP-2016
    Conference "Stochastic and analytic methods in Mathematical Physics"
    Yerevan, 4-11 September 2016
  • SMP-2016
    Summer school "Universality, Scaling Limits, and Effective Theories"
    Rome, 11-15 July 2016
  • CT-MQM-2016
    Workshop "Contemporary trends in the mathematics of Quantum Mechanics"
    Rome, 4-8 July 2016
  • TQD-2016
    Workshop "Trieste Quantum Days: solid, stat, et al"
    Trieste, 21-23 June 206
  • Solid Math 2016
    Conference "Solid Math"
    Aalborg, 26-28 May 2016
  • MCQM-2016
    School and workshop "Mathematical challenges in quantum mechanics"
    Bressanone, 8-13 February 2016
  • Toulouse-2015
    Workshop "Modelling and Numerics for Quantum Systems"
    Toulouse 2-4 September 2015
  • TQMS-2015
    Conference "Trails in Quantum Mechanics and Surroundings"
    Como, 8-10 July 2015
  • Dynamics Days 2015
    Conference "Dynamics Days Central Asia in Khiva"
    Khiva, 25-27 May 2015
  • SPMP 2014
    Conference "Selected Problems in Mathematical Physics, Statistical Mechanics, Many-Body Quantum Physics and PDEs "
    La Spezia, 1-5 September 2014
  • SOLID MATH 2014
    Conference "Solid Math"
    SISSA Trieste, 16-19 June 2014
  • MCZR 2014
    Workshop "Mathematical Challenges of zero-range Physics"
    CAS-LMU Munich, 26-28 February 2014
  • TQM 2013
    Conference "Trails in Quantum Mechanics and surroundings"
    Frascati, 29 January - 2 February 2013
  • TNCL 2011
    Workshop "Trails in a non-commutative land"
    SISSA Trieste, 18-20 May 20011
  • MMQM 2011
    Fourth School and Workshop on Mathematical Methods in Quantum Mechanics
    Bressanone, 16-21 February 2011
  • SDD 2010
    Workshop "Solitary and Dispersive Days"
    Milano, 13-17 December 2010
  • MMQM 2009
    School and Workshop on Mathematical Methods in Quantum Mechanics
    Bressanone, 16-21 February 2009
  • ATMP 2008
    Conference on Advances in Theoretical and Mathematical Physics
    Napoli, Istituto Italiano per gli Studi Filosofici, March 2008
  • MAQSA 2007
    Workshop "Multiscale Analysis for Quantum Systems"
    Roma, October 24th - 26th, 2007
  • IPS 2007
    Workshop "Interacting particle systems. A classical, quantum and stochastic perspective"
    Milano "Bicocca", October 22nd - 23rd, 2007
  • MMQM 2007
    School and Workshop "Mathematical Methods in Quantum Mechanics"
    Bressanone, February 26th - March 3rd, 2007
  • Boltzmann Symposium
    Atoms, Irreversibility and Entropy after 100 years: an appraisal of Boltzmann's ideas
    München, Germany, October 11th-13th, 2006
  • mpmMQ06
    Metodi e problemi matematici in Meccanica Quantistica
    Modena, October 5th-7th, 2006
  • DS_CQS06
    Dynamical Systems: Classical, Quantum and Stochastic
    Roma, Italy, October 2nd-5th, 2006
  • OTAMP 2006
    Operator Theory, Analysis and Mathematical

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