Related papers: The Quantum Effective Mass Hamilton-Jacobi Problem
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
I show that the classical Hamilton-Jacobi (H-J) equation can be used as a technique to study quantum mechanical problems. I first show that the the Schr\"odinger equation is just the classical H-J equation, constrained by a condition that…
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…
An appropriate extension of the effective potential theory is presented that permits the approximate calculation of the dynamical correlation functions for quantum systems. These are obtained by evaluating the generating functionals of the…
In the Kirchhoff model of a biopolymer, conformation dynamics can be described in terms of solitary waves, for certain special cross-section asymmetries. Applying this to the problem of electron transport, we show that the quantum effective…
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…
A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra. New mass-deformed versions of Scarf II, Morse and generalized…
In recent years it has been shown for hard sphere gas that, by retaining the correlation information, dynamical fluctuation and large deviation of empirical measure around Boltzmann equation could be proved, in addition to the classical…
Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the…
We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is…
Revisiting the issue associated with Position-Dependent Mass (PDM), we reaffirm that the appropriate framework for addressing a generic PDM is the symmetrization proposed by BenDaniel and Duke. To accomplish this result adopts the effective…
In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical…
The Effective One-Body formalism of the gravitational two-body problem in general relativity is reconsidered in the light of recent scattering amplitude calculations. Based on the kinematic relationship between momenta and the effective…
The analytic solutions of the one-dimensional Schroedinger equation for the trigonometric Rosen-Morse potential reported in the literature rely upon the Jacobi polynomials with complex indices and complex arguments. We first draw attention…
The search for a potential function $S$ allowing to reconstruct a given metric tensor $g$ and a given symmetric covariant tensor $T$ on a manifold $\mathcal{M}$ is formulated as the Hamilton-Jacobi problem associated with a canonically…
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
We derive the geodesic equation for point particles propagating in Moyal-type noncommutative spacetimes using a field-theoretic approach based on the quasi-classical limit of the noncommutative Klein-Gordon equation. Starting from a…
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 paper deals with Hawking radiation related to non-static spherically symmetric black hole. Quantum corrections are incorporated using Hamilton-Jacobi method beyond semi-classical approximation. It is found that different order…