相关论文: Analytical Solutions of the Quantum Hamilton-Jacob…
By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the…
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…
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…
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…
It is well known in classical mechanics that, the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. The equivalent quantum action variable…
In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrodinger equation. Then, in the case of separated variables, by requiring that the…
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…
The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family…
The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…
In this thesis, the quantum Hamilton Jacobi (QHJ) formalism is used to study various exactly solvable (ES) and quasi -exactly solvable (QES) models. Using this method, we obtain the bound state eigenvalues and the eigenfunctions for 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…
It is shown that by means of the approach based on the Quantum Hamilton-Jacobi equation, it is possible to modify the WKB expressions for the energy levels of quantum systems, when incorrect, obtaining exact WKB-like formulae. This extends…
An ordinary unambiguous integral representation for the finite propagator of a quantum system is found by starting of a privileged skeletonization of the functional action in phase space, provided by the complete solution of the…
The Hamilton-Jacobi method is generalized, both, in classical and relativistic mechanics. The implications in quantum mechanics are considered in the case of Klein-Gordon equation. We find that the wave functions of Klein-Gordon theory can…
Hamilton-Jacobi theory is a fundamental subject of classical mechanics and has also an important role in the development of quantum mechanics. Its conceptual framework results from the advantages of transformation theory and, for this…
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…
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…
A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing…
In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form'…
We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in…