Mathematical methods of Quantum Mechanics
Research topics
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Quantum mechanical description of a system subject to points, lines and surfaces interactions.
- Spectral analysis, properties of solutions, scattering.
- Multibody case.
- Time dependent case, in particular periodic.
- Exactly solvable models of ionization.
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Constrained systems and nano structures in Quantum Mechanics.
- Spectra and limit equations on graphs.
- Large N limit in Quantum Mechanics.
- Effective equations, existence and properties of the solutions.
- Non-linear Schrödinger equation.
- Phenomenon of ionization by a time-periodic potential: the long time behaviour.
- Mathematical study of the phenomenon known in Physics as "decoherence".
Joint projects
- NANOMATH
Mathematical Modeling and Numerical Analysis of Quantum Systems with Applications to Nanosciences (I.N.d.A.M. project 2006-2007)
Resources and manuals
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The Mathematics of Quantum Mechanics
by Kenji Yajima (in English)
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Elementi di Meccanica Quantistica
by Gianfausto Dell'Antonio (in Italian)
- Elements of Quantum Mechanics
by Gianfausto Dell'Antonio (in English, preliminary version)
Please report any suggestion or misprint to gianfa@sissa.it
Workshops and Conferences
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MAQM 2007
Workshop "Multiscale Analysis for Quantum Systems"
Roma, October 24th - 26th, 2007
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IPS 2007
Workshop "Interacting particle systems. A classical, quantum and stochastic perspective"
Milano "Bicocca", October 22nd - 23rd, 2007
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MMQM 2007
School and Workshop "Mathematical Methods in Quantum Mechanics"
Bressanone, February 26th - March 3rd, 2007
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NanoQ2006
Recent advances in the mathematical modeling and numerical simulation of nanoscale quantum semiconductor devices
Milano, November 30th - December 1st, 2006
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Boltzmann Symposium
Atoms, Irreversibility and Entropy after 100 years: an appraisal of Boltzmann's ideas
München, Germany, October 11th-13th, 2006
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mpmMQ06
Metodi e problemi matematici in Meccanica Quantistica
Modena, Italy, October 5th-7th, 2006
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DS_CQS06
Dynamical Systems: Classical, Quantum and Stochastic
Roma, Italy, October 2nd-5th, 2006
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OTAMP 2006
Operator Theory, Analysis and Mathematical Physics
Lund, Sweden, June 15th-22nd, 2006
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BEC and QI 2005
Workshop on Bose-Einstein Condensation and Quantum Information - E.S.I.
Wien, December 18th-20th, 2005
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Giornata di lavoro nanomath
Mathematical Modeling and Numerical Analysis of Quantum Systems with Applications to Nanosciences
Firenze, December 16th, 2005
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MMQM 2005
School and Workshop "Mathematical Methods in Quantum Mechanics"
Bressanone, February 21st-26th, 2005
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OWR 2005
Oberwolfach Workshop "Entanglement and Decoherence:
Mathematics and Physics of Quantum Information and Computation"
Oberwolfach, January 23rd-29th, 2005
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PMMQ 2003
Convegno Nazionale "Problemi Matematici in Meccanica Quantistica"
Modena, December 18th-20th, 2003
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Schrödinger 2003
Workshop on Spectral Problems for Schrödinger-type Operators
Trieste, March 11th-14th, 2003
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