A Class of Self-Trapped and Self-Focusing Wave Functions in Madelung Fluid Picture of A Single Free Particle Quantum System
نویسندگان
چکیده
Using the Madelung fluid picture of Schrödinger equation for a single free particle moving in one spatial dimension, we shall specify a class of wave functions whose quantum probability density is being trapped by the quantum potential it itself generates. The global convexity of the quantum potential generated by the initial self-trapped wave function will then be shown to further localize the quantum probability density through a selfgenerated focusing equation for a finite interval of time.
منابع مشابه
Scale invariant quantum potential leading to globally self-trapped wave function in Madelung fluid
We show in spatially one dimensional Madelung fluid that a simple requirement on local stability of the maximum of quantum probability density will, if combined with the global scale invariance of quantum potential, lead to a class of quantum probability densities globally being self-trapped by their own self-generated quantum potentials, possessing only a finite-size spatial support. It turns ...
متن کاملAnalytic solutions of the Madelung equation
We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential. 1 ar X iv :1 70 3. 10 48 2v 1 [ qu an tph ] 3 0 M ar 2 01 7
متن کاملBistability in the Electric Current through a Quantum-Dot Capacitively Coupled to a Charge-Qubit
We investigate the electronic transport through a single-level quantum-dot which is capacitively coupled to a charge-qubit. By employing the method of nonequilibrium Green's functions, we calculate the electric current through quantum dot at finite bias voltages. The Green's functions and self-energies of the system are calculated perturbatively and self-consistently to the second order of inte...
متن کاملSelf-dual Vortices in Chern-simons Hydrodynamics
The classical theory of non-relativistic charged particle interacting with U(1) gauge field is reformulated as the Schrödinger wave equation modified by the de-Broglie-Bohm quantum potential nonlinearity. For, (1 h̄) deformed strength of quantum potential the model is gauge equivalent to the standard Schrödinger equation with Planck constant h̄, while for the strength (1 + h̄), to the pair of diff...
متن کاملDynamical evolution of nonclassical properties in cavity quantum electrodynamics with a single trapped ion
In this paper, by considering a system consisting of a single two-level trapped ion interacting with a single-mode quantized radiation field inside a lossless cavity, the temporal evolution of the ionic and the cavity-field quantum statistical properties including photon-counting statistics, quantum fluctuations of the field quadratures and quantum fluctuations of the ionic dipole variables are...
متن کامل