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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Modified quantum trajectory dynamics using a mixed wave function representation.

Sophya Garashchuk¹, Vitaly A Rassolov

¹Department of Chemistry and Biochemistry, University of South Carolina, South Carolina 29208, USA.

The Journal of Chemical Physics

|November 6, 2004

Summary

Quantum trajectory dynamics, crucial for large quantum systems, are stabilized using a mixed coordinate/polar representation. This novel approach resolves singularities near wave function nodes, enabling accurate description of quantum interference.

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Area of Science:

Quantum mechanics
Computational chemistry
Theoretical physics

Background:

Quantum trajectory dynamics offer an efficient method for simulating quantum systems.
A key limitation is instability near wave function density nodes due to a singular quantum potential.

Purpose of the Study:

To develop a stable and accurate method for quantum trajectory dynamics.
To address the singularity issue in quantum potential near wave function nodes.

Main Methods:

A mixed coordinate space/polar representation of the wave function was employed.
This representation modifies the trajectory dynamics to be nonsingular and smooth.

Main Results:

The modified dynamics accurately describe wave function density nodes and interference patterns.
The approach is exact for wave functions with nodes in locally quadratic potentials.
An approximate version aligns with the semiclassical linearized quantum force method.

Conclusions:

The mixed representation successfully overcomes the instability of quantum trajectory dynamics.
This method provides an exact and stable framework for simulating quantum phenomena, particularly interference effects.