TY - RPRT
T1 - SchÃ¶dinger operators on half-line with shrinking potentials at the origin
Y1 - 2015
A1 - Gianfausto Dell'Antonio
A1 - Alessandro Michelangeli
AB - We discuss the general model of a SchrÃ¶dinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/34439
U1 - 34566
ER -
TY - JOUR
T1 - Some remarks on quantum mechanics
JF - International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018
Y1 - 2012
A1 - Gianfausto Dell'Antonio
KW - Quantum mechanics
AB - We discuss the similarities and differences between the formalism of Hamiltonian Classical Mechanics and of Quantum Mechanics and exemplify the differences through an analysis of tracks in a cloud chamber.
PB - World Scientific Publishing
UR - http://hdl.handle.net/1963/7018
U1 - 7013
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -
TY - JOUR
T1 - Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions
JF - Rev. Math. Phys. 24 (2012), 1250017
Y1 - 2012
A1 - Michele Correggi
A1 - Gianfausto Dell'Antonio
A1 - Domenico Finco
A1 - Alessandro Michelangeli
A1 - Alessandro Teta
AB - We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs.
PB - World Scientific
UR - http://hdl.handle.net/1963/6069
U1 - 5955
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - JOUR
T1 - Semiclassical analysis of constrained quantum systems
JF - J. Phys. A 37 (2004) 5605-5624
Y1 - 2004
A1 - Gianfausto Dell'Antonio
A1 - Lucattilio Tenuta
AB - We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar^(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system.
PB - IOP Publishing
UR - http://hdl.handle.net/1963/2997
U1 - 1336
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Statistics in space dimension two
JF - Lett. Math. Phys. 40 (1997), no. 3, 235-256
Y1 - 1997
A1 - Gianfausto Dell'Antonio
A1 - Rodolfo Figari
A1 - Alessandro Teta
AB - We construct as a selfadjoint operator the Schroedinger hamiltonian for a system of $N$ identical particles on a plane, obeying the statistics defined by a representation $\\\\pi_1$ of the braid group. We use quadratic forms and potential theory, and give details only for the free case; standard arguments provide the extension of our approach to the case of potentials which are small in the sense of forms with respect to the laplacian. We also comment on the relation between the analysis given here and other approaches to the problem, and also on the connection with the description of a quantum particle on a plane under the influence of a shielded magnetic field (Aharanov-Bohm effect).
PB - SISSA Library
UR - http://hdl.handle.net/1963/130
U1 - 12
U2 - LISNU
U3 - Interdisciplinary Laboratory for Advanced Studies
ER -