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Quantum Hamilton-Jacobi Formalism

Ashok Kumar Kapoor, Prasanta Kumar Panigrahi, S. Sree Ranjani

SpringerBriefs in physicsJan 1, 20220 citations

Quantum Hamilton-Jacobi Formalism

Ashok Kumar Kapoor, Prasanta Kumar Panigrahi, S. Sree Ranjani

SpringerBriefs in physicsJan 1, 20220 citations

Hamilton–Jacobi Formalism

Claude Gignoux, BERNARD SILVESTRE-BRAC

Springer eBooksJan 1, 20090 citations

On the quantum Hamilton-Jacobi formalism

Antonio S. de Castro, ALVARO DE SOUZA DUTRA

Foundations of PhysicsJun 1, 19918 citations

A note on the quantum Hamilton-Jacobi formalism

E. Elizalde

Foundations of Physics LettersJun 1, 19933 citations

The Quantum Hamilton–Jacobi Equation and the Link Between Classical and Quantum Mechanics

M. Fusco Girard

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 classical ones, this is not the case in the allowed regions. There, the limit is reached only if the quantum fluctuations are eliminated by means of coarse-graining averages. Analogously, the classical Hamilton–Jacobi scheme bringing to the motion's equations arises from a similar formal quantum procedure. Quanta 2022; 11: 42–52.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 classical ones, this is not the case in the allowed regions. There, the limit is reached only if the quantum fluctuations are eliminated by means of coarse-graining averages. Analogously, the classical Hamilton–Jacobi scheme bringing to the motion's equations arises from a similar formal quantum procedure. Quanta 2022; 11: 42–52.

arXiv:2203.07005QuantaNov 3, 20223 citations

Epistemic Uncertainty from an Averaged Hamilton–Jacobi Formalism

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