Related papers: Unstable particles in non-relativistic quantum mec…
We present a detailed non-perturbative analysis of the time-evolution of a well-known quantum-mechanical system - a particle between potential walls - describing the decay of unstable states. For sufficiently high barriers, corresponding to…
Schroedinger equations with position dependent mass which are scale invariant and admit second order integrals of motion are classified.
This paper undertakes a study of the nature of the force associated with the local U (1) gauge symmetry of a non-relativistic quantum particle. To ensure invariance under local U (1) symmetry, a matter field must couple to a gauge field. We…
Using elements of symmetry, we constructed the Noncommutative Schr\"odinger Equation from a representation of Exotic Galilei Group. As consequence, we derive the Ehrenfest theorem using noncommutative coordinates. We also have showed others…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
We show how the state of an unstable particle can be defined in terms of stable asymptotic states. This general definition is used to discuss and to solve some old problems connected with the short-time and large-time behaviour of the…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
In this article the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs.…
Relativistic Schroedinger Theory (RST), as a general gauge theory for the description of relativistic N-particle systems, is shown to be a mathematically consistent and physically reasonable framework for an arbitrary assemblage of positive…
We theoretically investigate the phenomenon of modulation instability for systems obeying nonlinear Schr\"odinger equation, which are under the influence of an external homogeneous synthetic magnetic field. For an initial condition, the…
We show that a possible violation of the Robertson-Schr\"odinger uncertainty principle may signal the existence of a deformation of the Heisenberg-Weyl algebra. More precisely, we prove that any Gaussian in phase-space (even if it violates…
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei…
We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…
In the framework of special relativity, all particles are point-like or string-like. This nature of particles has caused the divergence difficulties in quantum field, string and superstring theories. In the framework of special relativity,…
An important and well established area of quantum optics is the theory of Markovian stochastic Schr\"odinger equations (or by another name quantum trajectory theory). Recently stochastic Schr\"odinger equations have been developed for…
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are…
The standard argument for the validity of Einstein's equivalence principle in a non-relativistic quantum context involves the application of a mass superselection rule. It is surprising that the consistency between such an important…
We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In…