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Short-time quantum propagator and Bohmian trajectories
Maurice de Gosson1, Basil Hiley
1Universität Wien, Fakultät für Mathematik, NuHAG, Wien 1090, Austria.
Physics Letters. A
|December 10, 2013
Summary
Quantum mechanics becomes classical at very short times. This study refines short-time action expressions, showing the quantum potential is negligible for point sources, validating prior observations and simplifying quantum motion analysis.
Area of Science:
- Quantum mechanics
- Theoretical physics
- Mathematical physics
Background:
- The Makri-Miller formalism provides a basis for calculating quantum actions.
- Previous observations regarding the quantum potential's behavior have been largely overlooked.
Purpose of the Study:
- To derive accurate expressions for the quantum propagator at short times.
- To investigate the significance of the quantum potential in short-time quantum dynamics.
- To validate a previously ignored observation concerning the quantum potential.
Main Methods:
- Utilizing corrected short-time action expressions derived from the Makri-Miller work.
- Deriving an accurate expression for the quantum propagator modulo ħ.
- Analyzing the behavior of the quantum potential for a point source.
Main Results:
- An accurate expression for the quantum propagator modulo ħ was derived.
- The quantum potential was shown to be negligible modulo ħ for a point source.
- This finding supports a largely ignored observation by Holland.
Conclusions:
- The quantum potential's negligibility at short times for point sources simplifies quantum motion analysis.
- Quantum motion approximates classical motion for extremely short time intervals.
- This work validates and emphasizes the importance of Holland's earlier findings in quantum dynamics.
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