Related papers: Classical trajectories compatible with quantum mec…
This work proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schr\"odinger…
The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to…
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large…
In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2…
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
Quantum state estimation, based on the numerical integration of stochastic master equations (SMEs), provides estimates for the evolution of quantum systems subject to continuous weak measurements. The approach is similar to classical state…
We show that the average trajectories of relativistic quantum particles in Schwarzschild spacetime, obtained via quantum mechanical weak measurements of momentum and energy, are equivalent to the predicted flow lines of probability current…
Here the ionization and high harmonic generation in Hydrogen and Helium by using quantum (hydrodynamic) trajectories is analyzed theoretically. The quantum trajectories allow a self-contained treatment of the electron exchange and…
The behavior of classical monochromatic waves in stationary media is shown to be ruled by a novel, frequency-dependent function which we call Wave Potential, and which we show to be encoded in the structure of the Helmholtz equation. An…
Stochastic mechanics (SM), as proposed by Edward Nelson and others in the 20th century, aims to reconstruct quantum mechanics (QM) from a more fundamental theory of classical point particles interacting with a classical-like ether, where…
The concepts of quantile position, trajectory, and velocity are defined. For a tunneling quantum mechanical wave packet, it is proved that its quantile position always stays behind that of a free wave packet with the same initial…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or…
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless…
The complex processes leading to the collisional population of ultra-long-lived Rydberg states with very high angular momentum can be explained surprisingly well using classical mechanics. In this article, we explain the reason behind this…
It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz…
Are the classical singularities of general relativistic spacetimes, normally defined by the incompleteness of classical particle paths, still singular if quantum mechanical particles are used instead? This is the question we will attempt to…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and…