aqora

Quantization from Hamilton–Jacobi theory with a random constraint

Agus Budiyono

arXiv:1205.0244Physica A Statistical Mechanics and its ApplicationsMay 26, 201211 citations

Hamilton—Jacobi quantization of constrained systems

D. Băleanu, Y. Güler

Czechoslovak Journal of PhysicsDec 1, 20010 citations

Hamilton-Jacobi Quantization Of Christ - Lee Model

F. M. Al Saba, Hassan Harb, Sami I. Muslih

مجلة جامعة الأقصى سلسلة العلوم الإنسانيةJan 1, 20030 citations

Geometric phase within the complex quantum Hamilton–Jacobi formalism

Chia‐Chun Chou, Róbert E. Wyatt

Physics Letters AApr 23, 20102 citations

Improved Hamilton-Jacobi Quantization for a Nonholonomic System

홍순태, WonTaeKim, 박영재 +1 more

Dec 1, 20030 citations

Simple derivations of the Hamilton–Jacobi equation and the eikonal equation without the use of canonical transformations

Alex Small, Kai S. Lam

The Hamilton–Jacobi equation in classical mechanics and the related eikonal equation in geometrical optics are often described as the “point of closest approach” between classical and quantum mechanics. Most textbook treatments of Hamilton–Jacobi theory are aimed at graduate students and derive the equation only after a long introduction to canonical transformations. Most treatments of the eikonal equation only emphasize its use in geometrical optics. We show that both the Hamilton–Jacobi equation and the eikonal equation can be derived by a common procedure using only elementary aspects of the Lagrangian and Hamiltonian formalisms introduced in undergraduate classical mechanics courses. Through this common approach, we hope to highlight to undergraduates the deep connections between classical mechanics, classical wave theory, and Schrödinger’s wave mechanics.The Hamilton–Jacobi equation in classical mechanics and the related eikonal equation in geometrical optics are often described as the “point of closest approach” between classical and quantum mechanics. Most textbook treatments of Hamilton–Jacobi theory are aimed at graduate students and derive the equation only after a long introduction to canonical transformations. Most treatments of the eikonal equation only emphasize its use in geometrical optics. We show that both the Hamilton–Jacobi equation and the eikonal equation can be derived by a common procedure using only elementary aspects of the Lagrangian and Hamiltonian formalisms introduced in undergraduate classical mechanics courses. Through this common approach, we hope to highlight to undergraduates the deep connections between classical mechanics, classical wave theory, and Schrödinger’s wave mechanics.

American Journal of PhysicsMay 13, 20118 citations

Geometric quantization and Hamilton-Jacobi theory

Related papers

Geometric quantization and Hamilton-Jacobi theory

Related papers