01018nas a2200121 4500008004100000245007900041210007000120260001000190520058700200100002900787700002900816856005100845 2015 en d00aSchödinger operators on half-line with shrinking potentials at the origin0 aSchödinger operators on halfline with shrinking potentials at th bSISSA3 aWe discuss the general model of a Schrödinger 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.1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3443900568nas a2200121 4500008004100000245003800041210003800079260003200117520021000149653002200359100002900381856003600410 2012 en d00aSome remarks on quantum mechanics0 aSome remarks on quantum mechanics bWorld Scientific Publishing3 aWe 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.10aQuantum mechanics1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/701801607nas a2200157 4500008004100000245009600041210006900137260002100206520106500227100002201292700002901314700002001343700002901363700002101392856003601413 2012 en d00aStability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions0 aStability for a System of N Fermions Plus a Different Particle w bWorld Scientific3 aWe 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.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://hdl.handle.net/1963/606900849nas a2200121 4500008004300000245005800043210005800101260001900159520046100178100002900639700002300668856003600691 2004 en_Ud 00aSemiclassical analysis of constrained quantum systems0 aSemiclassical analysis of constrained quantum systems bIOP Publishing3 aWe 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.1 aDell'Antonio, Gianfausto1 aTenuta, Lucattilio uhttp://hdl.handle.net/1963/299701073nas a2200133 4500008004100000245003800041210003800079260001800117520069900135100002900834700002000863700002100883856003500904 1997 en d00aStatistics in space dimension two0 aStatistics in space dimension two bSISSA Library3 aWe 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).1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/130