相关论文: From interpretation of the three classical mechani…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their…
We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
We develop a classical theoretical description for nonlinear many-body dynamics that incorporates the back-action of a continuous measurement process. The classical approach is compared with the exact quantum solution in an example with an…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
The idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar \omega $ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
Motivated by various systems in which quantum effects occur in classical backgrounds, we consider the dynamics of a classical particle as described by a coherent state that is coupled to a quantum bath via bi-quadratic interactions. We…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…
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 amplitude, Born rule,…
Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
The Schr\"odinger's wave function can naturally be realized as an 'instantaneous resonant spatial mode' in which quantum particle moves and hence the Born's rule is derived after identifying its origin. This realization facilitates the…
A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…