Related papers: Entwined Pairs and Schroedinger 's Equation
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…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…
We prove a global well-posedness result for defocusing nonlinear Schrodinger equations with time dependent potential. We then focus on time dependent harmonic potentials. This aspect is motivated by Physics (Bose--Einstein condensation),…
We study a family of coherent states, called Schr\"odingerlets, both in the continuous and discrete setting. They are defined in terms of the Schr\"odinger equation of a free quantum particle and some of its invariant transformations.
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
The particle in an expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation. An angle dependent potential is proposed accurately describing the mechanical behavior while also…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…
We present solutions of the time dependent Schrodinger equation for a SQUID ring coupled to an electromagnetic field, both treated quantum mechanically. We that show the SQUID ring can be used to create a maximally entangled state with the…
The Schwinger mechanism of electron-positron pair production in the presence of strong external electric fields is analyzed numerically for the case of one- and two-dimensional field configurations where the external field depends both on…
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…
The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…
If time has three dimensions, how does a particle move? This paper demonstrates that quantum physics naturally emerges from a framework of three-dimensional time. We present the equations governing the motion of 0-spin, 1-spin, and 1/2-spin…
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…
We analyze the spins of a Schwinger particle pair in a spatially uniform but time dependent electric field. The particle pair's spins are in the maximally entangled Bell state only if the particles' momenta are parallel to the electric…
Quantum lattice models describe a wide array of physical systems, and are a canonical way to numerically solve the Schrodinger equation. Here we prove the potential inversion theorem, which says that wavefunction probability in these models…
The Schrodinger motion of a charged quantum particle in an electromagnetic potential can be simulated by the paraxial dynamics of photons propagating through a spatially inhomogeneous medium. The inhomogeneity induces geometric effects that…
The free particle Schrodinger equation admits a non-trivial self-accelerating Airy wave packet solution. Recently, the Airy beams that freely accelerate in space was experimentally realized in photonics community. Here we present…