Related papers: Relativistic Bohmain Mechanics
It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz…
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 construct a relativistic quantum mechanics for a boson. To do this we exploit two component wave functions in Dirac type equations of motion. In our formalism we fix the pathological aspect of particle probability density which appears…
A de Broglie-Bohm like model of Klein-Gordon equation, that leads to the correct Schrodinger equation in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum potential, the main…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
Given a normalized state-vector $\psi $, we define the conditional expectation $\mathbb{E }_{\psi } (A | B ) $ of a Hermitian operator $A $ with respect to a strongly commuting family of self-adjoint operators $B $ as the best…
The theoretical foundations of quantum mechanics and de Broglie-Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal…
de Broglie-Bohm theory (dBBT), treating quantum particles as point objects moving along well defined (Bohmian) trajectories, offers an appealing solution of the measurement problem in quantum mechanics; it has, however, problems relating to…
A recent article claims to measure the speed of quantum particles in the classically forbidden regime where the energy of the particles is lower than the local potential, and further claims that the results of this experiment challenge…
A novel perspective on relativistic transformation recently-proposed provides an insight into the very meaning of the principle of relativity. With this novel perspective and Bell's theorem, we argue that special relativity, instead of…
The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex valued Gaussian, looking for relevance to quantum mechanics. Here we show that the…
Following de Broglie and Vigier, a fully relativistic causal interpretation of quantum mechanics is given within the context of a geometric theory of gravitation and electromagnetism. While the geometric model shares the essential…
Students in a quantum mechanics course are often introduced to the Schr\"odinger equation as the standard mathematical tool. However, rarely do students develop an understanding as to why the equation is the choice for modeling quantum…
We discuss the Bohmian mechanics by means of the deformed Schr\"odinger equation for position dependent mass, in the context of a $q$-algebra inspired by nonextensive statistics. A deduction of the Bohmian quantum formalism is performed by…
We consider for clarity the simple case of the one dimensional non-relativistic Schr\"{o}dinger equation and regard it as an ensemble mean representation of the stochastic motion of a single particle in a vacuum, subject to an undefined…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
The de Broglie - Bohm Interpretation of Quantum Mechanics assigns positions and trajectories to particles. We analyze the validity of a formula for the velocities of Bohmian particles which makes the analysis of these trajectories…
The de Broglie-Bohm interpretation of quantum mechanics and quantum field theory is generalized in such a way that it describes trajectories of relativistic fermionic particles and antiparticles and provides a causal description of the…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
We expose the Schr\"odinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schr\"odinger, Pauli and Dirac equations, as well as…