Related papers: Modified de Broglie-Bohm approach to quantum mecha…
We describe the quantum dynamics of the Hubbard model at semi-classical level, by implementing the Time-Dependent Variational Principle (TDVP) procedure on appropriate macroscopic wavefunctions constructed in terms of su(2)-coherent states.…
Bohmian mechanics supplements the quantum wavefunction with deterministic particle trajectories, offering an alternate, dynamical language for quantum theory. However, the Bohmian particle does not affect its guiding wave, so the wave field…
This paper describes a tentative relativistic quantum mechanics approach inspired by Dirac's point-form, which is based on the physics description on a hyperboloid surface. It is mainly characterized by a non-standard relation of the…
We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
Generalizing de Broglie's hypothesis, we show that the basic quantum behavior of ordinary field theory can be retrieved in a semi-classical and geometrical way from the assumption of intrinsic periodicity of elementary systems. The…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
Attempts for a geometrical interpretation of Quantum Theory were made, notably the deBroglie-Bohm formulation. This was further refined by Santamato who invoked Weyl's geometry. However these attempts left a number of unanswered questions.…
In this work we analyze recent proposals by Das and D\"{u}rr (DD) to measure the arrival time distributions of quantum particles within the framework of de Broglie Bohm theory (or Bohmian mechanics). We also analyze the criticisms made by…
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…
Minimum-time quantum control protocols can be obtained from the quantum brachistochrone formalism [Carlini, Hosoya, Koike, and Okudaira, Phys. Rev. Lett. 96, 06053, (2006)]. We point out that the original treatment implicitly applied the…
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
In the de Broglie - Bohm formulation of quantum mechanics, the electron is stationary in the ground state of the hydrogen atom, because the quantum force exactly cancels the Coulomb attraction of the electron to the proton. In this paper it…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Much attention has been drawn to quantum computing and the exponential speed-up in computation the technology would be able to provide. Various claims have been made about what aspect of quantum mechanics causes this speed-up. Formulations…
The physical consequences of the analysis performed in Parts I-IV are outlined within a scheme of the complete quantum (wave) mechanics called quantum field mechanics and completing the original ideas of Louis de Broglie by the dynamic…