Related papers: Modified Born-Jordan Method For Constructing The C…
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…
We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background…
It is shown that the time-energy uncertainty relation can be combined into the position-momentum uncertainty relation covariantly in the quark model of hadrons. This leads to a Lorentz-invariant form of the uncertainty relations. This model…
This article presents the derivation of a comprehensive formula for the Clebsch-Gordan coefficients in a quantum system. The formula is derived by employing the iterative application of angular momentum ladder operators on each defined…
Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition…
Recent developments in quantum computing suggest that it could be possible to make conditional changes to the state of a quantum mechanical system without resorting to classical observation. It is accomplished through collective response of…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
In this work, we refine the Bohr model of the hydrogen atom by describing the motion of the electron through a single real-valued stochastic process, effectively realizing Brownian motion under the Born rule. Our approach derives the…
The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This…
We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact.…
Probabilities in quantum theory are traditionally given by Born's rule as the expectation values of projection operators. Here it is shown that Born's rule is insufficient in universes so large that they contain identical multiple copies of…
We suggest and describe how to analyze new types of experiments that would test a proposed model of the quantum measurement process. That model produces the Born Rule as a corollary, and so agrees with conventional quantum predictions. The…
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate…
Starting from a Born-Oppenheimer decomposition of the Wheeler-DeWitt equation for the quantum cosmology of the matter-gravity system, we have performed a Wigner-Weyl transformation and obtained equations involving a Wigner function for the…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
Phase spaces as given by the Wigner distribution function provide a natural description of infinite-dimensional quantum systems. They are an important tool in quantum optics and have been widely applied in the context of time-frequency…
I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
A quantum dot proposal for the implementation of topological quantum computation is presented. The coupling of the electron charge to an external magnetic field via the Aharonov-Bohm effect, combined with the control dynamics of a double…
We showed in a recent article (Lawrence et. al., 2023, Quantum 7, 1015), that relative facts (outcomes), a central concept in Relational Quantum Mechanics, are inconsistent with Quantum Mechanics. We proved this by constructing a…