Related papers: Obtaining the Probability Vector Current Density i…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical…
It is shown how the essentials of quantum theory, i.e., the Schroedinger equation and the Heisenberg uncertainty relations, can be derived from classical physics. Next to the empirically grounded quantisation of energy and momentum, the…
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions…
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…
The quantum theories of boson and fermion fields with quadratic nonstationary Hamiltoanians are rigorously constructed. The representation of the algebra of observables is given by the Hamiltonian diagonalization procedure. The sufficient…
We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum…
The quantum backflow effect is a counterintuitive behavior of the probability current of a free particle, which may be negative even for states with vanishing negative momentum component. Here we address the notion of nonclassicality…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables (the current density and the superconducting order parameter, respectively) are included in the…
A method to derive the charge current density and its quantum mechanical correlation from the scattering matrix is discussed for quantum scattering systems described by a time-dependent Hamiltonian operator. The current density and charge…
The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an "Operational Epistemic Theory". In such context the quantum superposition principle has an extraneous…
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…