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Potential energy function information from quantum phase shift using the variable phase method.

Nelson H T Lemes1, João P Braga, Márcio O Alves

  • 1Instituto de Química, Universidade Federal de Alfenas, Rua Gabriel Monteiro da Silva 700 - Centro, Alfenas, MG, 37130-000, Brazil.

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This study introduces a new method for analyzing quantum phase shift sensitivity to potential energy functions. The approach simplifies calculations and significantly improves the accuracy of recovered potential energy functions.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Scattering theory

Background:

  • Quantum phase shifts are crucial for understanding atomic and molecular interactions.
  • Sensitivity analysis of potential energy functions is essential for accurate theoretical predictions.
  • Existing methods like finite difference can be computationally intensive.

Purpose of the Study:

  • To develop a more efficient and exact method for quantum phase shift sensitivity analysis.
  • To refine potential energy functions for improved accuracy.
  • To establish a foundation for recovering potential energy functions in higher dimensions.

Main Methods:

  • Established a set of differential equations for the functional derivative of the quantum phase shift.
  • Coupled these equations with the variable phase equation.
  • Integrated the established equations to analyze sensitivity accumulation.

Main Results:

  • Developed a straightforward procedure for establishing the sensitivity matrix.
  • Demonstrated accumulation of sensitivity phase shift with interatomic distance.
  • Reduced average error in phase shift from 9.8% to 0.13% by refining the potential energy function.

Conclusions:

  • The proposed method offers a simpler and more direct alternative to finite difference approaches.
  • The technique significantly enhances the accuracy of potential energy function recovery.
  • This work is a key step towards recovering potential energy functions from experimental data and in complex systems.