Related papers: Wave-particle duality and the Hamilton action
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behavior.…
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (nondispersive oscillating/spinning solitons), displaying simultaneous particle-like and…
In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle…
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…
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…
The Hamilton-Jacobi theory of Classical Mechanics can be extended in a novel manner to systems which are fuzzy in the sense that they can be represented by wave functions. A constructive interference of the phases of the wave functions then…
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…
We present the analytic solution for the stationary quantum HamiltonJacobi equation. Knowing the strong relation between the Riccati and quantum Hamilton-Jacobi equations, we develop a simple method to obtain the exact solution. Then, in…
A Hamiltonian formulation for the classical problem of electromagnetic interaction of two charged relativistic particles is found.
For one dimensional motions, we derive from the Dirac Spinors Equation (DSE) the Quantum Stationary Hamilton-Jacobi Equation for particles with spin 1/2. Then, We give its solution. We demonstrate that the $QSHJES_{1\over2}$ have two…
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In…
In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
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…
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…
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…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is…
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous…
This paper examines the physical meaning of the wave function in Bohmian mechanics (BM), addressing the debate between causal and nomological interpretations. While BM postulates particles with definite trajectories guided by the wave…