Related papers: QHJ, WKB and exact quantisation
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the…
In the present paper, we provide a detailed derivation of the stochastic Hamilton-Jacobi-Bellman equation
As a continuation of Rabei et al. work [11], the Hamilton- Jacobi partial differential equation is generalized to be applicable for systems containing fractional derivatives. The Hamilton- Jacobi function in configuration space is obtained…
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…
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 geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…
The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to…
The bound state wave functions for a wide class of exactly solvable potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is shown that, exploiting the singularity structure of the quantum momentum function, until now…
Using quantum Hamilton-Jacobi formalism of Leacock and Padgett, we show how to obtain the exact eigenvalues for supersymmetric (SUSY) potentials.
In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then…
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Mechanical systems (i.e., one-dimensional field theories) with constraints are the focus of this paper. In the classical theory, systems with infinite-dimensional targets are considered as well (this then encompasses also higher-dimensional…
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
We propose a heuristic method to obtain the approximate groundstate for a Hamiltonian in the qubit form, based on the stabilizer formalism. These states may serve as proper initial states for further refined computation. It would be…
The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this…
This paper presents the theory of Bohr-Sommerfeld-Heisenberg quantization of a completely integrable Hamiltonian system in the context of geometric quantization. The theory is illustrated with several examples.
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…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
We briefly review a hamiltonian path integral formalism developed earlier by one of us. An important feature of this formalism is that the path integral quantization in arbitrary co-ordinates is set up making use of only classical…