相关论文: Schroedinger revisited:How the time-dependent wave…

It is shown how the time-dependent Schr\"{o}dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics.…

An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable,…

Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…

In this work, we follow the idea of the De Broglie's matter waves and the analogous method that Schr\"{o}dinger founded wave equation, but we apply the more essential Hamilton principle instead of the minimum action principle of Jacobi…

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…

We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such…

The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…

Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of…

Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…

We reexamine the general solution of a Schr\"{o}dinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space…

From classical stochastic equations of motion we derive the quantum Schr\"odinger equation. The derivation is carried out by assuming that the real and imaginary parts of the wave function $\phi$ are proportional to the coordinates and…

With an apparent delay of over one century with respect to the development of standard Analytical Mechanics, but still in fully classical terms, the behavior of classical monochromatic wave beams in stationary media is shown to be ruled by…

Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…

Most authors of textbooks on quantum mechanics either postulate or sketch a short `ad hoc` derivation of Schrodinger's equation. In this work we give a detailed derivation of Schrodinger's equation from the Hamilton-Jacobi equation and the…

A new class of time-energy uncertainty relations is directly derived from the Schr\"odinger equations for time-dependent Hamiltonians. Only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full…

The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the…

Here I show that a classical or quantum bit state plus one simple operation, an action, are sufficient ingredients to derive a quantum dynamical equation that rules the sequential changes of the state. Then, by assuming that a freely moving…

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…

It is shown that for a relativistic particle moving in an electromagnetic field its equations of motion written in a form of the second law of Newton can be reduced with the help of elementary operations to the Hamilton-Jacobi equation. The…