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Quantum trajectories in complex space: one-dimensional stationary scattering problems.

Chia-Chun Chou1, Robert E Wyatt

  • 1Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, TX 78712, USA. chiachun@mail.utexas.edu

The Journal of Chemical Physics
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Summary
This summary is machine-generated.

This study explores quantum Hamilton-Jacobi formalism for scattering problems, revealing universal structures in complex quantum trajectories and potentials. Findings show consistent second-order pole structures in reflection regions across different potentials.

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Area of Science:

  • Quantum mechanics
  • Theoretical physics
  • Scattering theory

Background:

  • The quantum Hamilton-Jacobi formalism offers a unique perspective on quantum dynamics.
  • Understanding scattering phenomena is crucial for various areas of physics.

Purpose of the Study:

  • To investigate one-dimensional time-independent scattering problems using the quantum Hamilton-Jacobi formalism.
  • To derive and analyze equations for quantum trajectories and their relation to quantum momentum.
  • To explore the general properties and structures of complex quantum trajectories and potentials.

Main Methods:

  • Derivation of equations for local approximate quantum trajectories near stagnation points.
  • Numerical integration of equations of motion to determine exact complex quantum trajectories.
  • Analysis of quantum potentials and their pole structures in complex space.

Main Results:

  • Complex quantum trajectories exhibit diverse behaviors, including penetration into nonclassical regions and spiraling into attractors/repellers.
  • Classical potentials show varied pole structures in complex space.
  • Quantum potentials consistently display a second-order pole structure in the reflection region for the studied problems.

Conclusions:

  • Complex quantum trajectories and quantum potentials share general properties and similar structures across different one-dimensional scattering problems.
  • The quantum Hamilton-Jacobi formalism provides insights into the universal behavior of quantum systems in scattering scenarios.