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Quantum Hamilton-Jacobi theory
Marco Roncadelli1, L S Schulman
1INFN, Sezione di Pavia, Via A. Bassi 6, I-27100 Pavia, Italy. marco.roncadelli@pv.infn.it
Physical Review Letters
|November 13, 2007
Summary
Researchers have solved the quantum Hamilton-Jacobi equation (QHJE) by using the Schrödinger equation
Area of Science:
- Quantum mechanics
- Theoretical physics
- Mathematical physics
Background:
- Quantum canonical transformations are fundamental in quantum theory.
- Solving the nonlinear operator partial differential equation of the quantum Hamilton-Jacobi equation (QHJE) has been a significant challenge.
- This difficulty has limited the practical application of quantum Hamilton-Jacobi theory.
Purpose of the Study:
- To overcome the challenge of solving the quantum Hamilton-Jacobi equation (QHJE).
- To enable the practical application of quantum Hamilton-Jacobi theory.
- To explore the relationship between operator ordering and path density in semiclassical trajectories.
Main Methods:
- Developing a novel prescription to construct solutions for the QHJE.
- Utilizing the propagator of the associated Schrödinger equation as a starting point.
- Applying the derived solutions to investigate operator ordering and path density.
Main Results:
- A straightforward method for solving the QHJE has been established.
- Solutions to the QHJE can be directly constructed from the Schrödinger equation's propagator.
- A novel connection between operator ordering and the density of paths near semiclassical trajectories has been revealed.
Conclusions:
- The developed method simplifies the solution of the QHJE, paving the way for its practical use.
- This breakthrough opens new avenues for research in quantum canonical transformations and quantum dynamics.
- The findings offer new insights into the interpretation of quantum mechanics and semiclassical approximations.
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