Related papers: A subluminous Schroedinger equation
Now that we have reached the centennial of Erwin Schrodinger's seminal paper introducing the wavefunction theory of matter, it is right and proper to inquire as to its legacy. It is undeniable that today every paper in atomic physics cites…
A nonlinear generalisation of Schrodinger's equation is obtained using information-theoretic arguments. The nonlinearities are controlled by an intrinsic length scale and involve derivatives to all orders thus making the equation mildly…
Feynman's path integral formulation arose from his attempt to incorporate the Lagrangian framework into quantum mechanics, offering what he regarded as a more fundamental perspective than the Hamiltonian approach, particularly in the…
Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R^d. The particle is accelerated by a constant external field; when colliding with an obstacle, the particle inelastically…
Adding a constant energy offset leaves classical dynamics unchanged. In quantum mechanics it changes the phase velocity of the wavefunction. The inclusion of the constant rest energy in the Klein-Gordon formulation leads to significantly…
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
Optical lossless beam splitters are frequently encountered in fundamental physics experiments regarding the nature of light, including "which-way" determination of light particles, N. Bohr's complementarity principle, or the EPR paradox and…
It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show…
In Bohmian mechanics, a version of quantum mechanics that ascribes world lines to electrons, we can meaningfully ask about an electron's instantaneous speed relative to a given inertial frame. Interestingly, according to the relativistic…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…
We consider a quantum wire with two subbands of spin-polarized electrons in the presence of strong interactions. We focus on the quantum phase transition when the second subband starts to get filled as a function of gate voltage. Performing…
It is well-known that the coordinate as a continuous variable, consisting of a set of all points between 0 and $L$ contradicts the observability of measurement. In other words there might exist a fundamental length in nature, such as the…
We address the universal applicability of the discrete nonlinear Schroedinger equation. By employing an original but general top-down/bottom-up procedure based on symmetry analysis to the case of optical lattices, we derive the most widely…
The propagation of a wave-packet in a nonlinear disordered medium exhibits interesting dynamics. Here, we present an analysis based on the nonlinear Schr\"odinger equation (Gross-Pitaevskii equation). This problem is directly connected to…
Consider a non-relativistic quantum particle with wave function inside a region $\Omega\subset \mathbb{R}^3$, and suppose that detectors are placed along the boundary $\partial \Omega$. The question how to compute the probability…
We propose a first order equation from which the Schrodinger equation can be derived. Matrices that obey certain properties are introduced for this purpose. We start by constructing the solutions of this equation in 1D and solve the problem…
Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear…
We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge…
Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction…