Related papers: Energy-dependent noncommutative quantum mechanics
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
We analyse the Klein-Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting…
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…
We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…
Stochastic extensions of the Schrodinger equation have attracted attention recently as plausible models for state reduction in quantum mechanics. Here we formulate a general approach to stochastic Schrodinger dynamics in the case of a…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
The study of the Schr\"{o}dinger equation with the position-dependent effective mass has attracted a lot of attention, due to its applications in many fields of physics, including the properties of the semiconductors, semiconductor…
Analytical expressions for the transition probability and the energy spectrum of the 1D Schr\"odinger equation with position dependent mass are presented for the triangular quantum barrier and quantum well. The transmission coefficient is…
An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the…
The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
A closed-form solution to the energy-based stochastic Schrodinger equation with a time-dependent coupling is obtained. The solution is algebraic in character, and is expressed directly in terms of independent random data. The data consist…
Our main focus is to explore different models in noncommutative spaces in higher dimensions. We provide a procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables…
We construct a new nonlinear deformed Schr\"odinger structure using a nonlinear derivative operator which depends on a parameter $q$. This operator recovers Newton derivative when $q \rightarrow 1$. Using this operator we propose a deformed…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-form solution to the dynamical equation, valid for all…