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The phenomenon that a quantum particle propagating in a detector, such as a Wilson cloud chamber, leaves a track close to a classical trajectory is analyzed. We introduce an idealized quantum-mechanical model of a charged particle that is periodically illuminated by pulses of laser light resulting in repeated indirect measurements of the approximate position of the particle. For this model we present a mathematically rigorous analysis of the appearance of particle tracks, assuming that the Hamiltonian of the particle is quadratic in the position- and momentum operators, as for a freely moving particle or a harmonic oscillator.
We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schroedinger operator.
The classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M.C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point symmetries of the
In this paper we provide a detailed description of the eigenvalue $ E_{D}(x_0)leq 0$ (respectively $ E_{N}(x_0)leq 0$) of the self-adjoint Hamiltonian operator representing the negative Laplacian on the positive half-line with a Dirichlet (resp. Neum
We describe coherent states and associated generalized Grassmann variables for a system of $m$ independent $q$-boson modes. A resolution of unity in terms of generalized Berezin integrals leads to generalized Grassmann symbolic calculus. Formulae for
For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schrodinger equation consists of several equations, one for each time variable. This leads to the