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Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
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Variational Solutions for Resonances by a Finite-Difference Grid Method.

Roie Dann1, Guy Elbaz2, Jonathan Berkheim3

  • 1The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel.

Molecules (Basel, Switzerland)
|September 10, 2021
PubMed
Summary
This summary is machine-generated.

We modified the finite difference grid method (FDM) to calculate molecular resonances, which are metastable states. This approach enables the study of complex poles, providing energies and lifetimes for chemical systems.

Keywords:
finite difference methodgrid methodsresonancesvariational principle

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • The finite difference grid method (FDM) is a numerical technique used in computational chemistry.
  • Calculating resonances, which represent metastable states with finite lifetimes, is crucial for understanding chemical dynamics.
  • Existing methods may have limitations in accurately determining resonance properties.

Purpose of the Study:

  • To modify the finite difference grid method (FDM) to satisfy the variational principle.
  • To enable the calculation of both real and complex poles of the scattering matrix.
  • To incorporate FDM into the study of resonance phenomena in chemistry.

Main Methods:

  • Modification of the finite difference grid method (FDM) to incorporate the variational principle.
  • Calculation of real and complex poles of the scattering matrix.
  • Application to systems exhibiting resonance phenomena.

Main Results:

  • Demonstrated that the modified FDM can satisfy the variational principle.
  • Enabled the calculation of complex poles, identified as resonances.
  • Provided a method to determine energies and inverse lifetimes of metastable states.

Conclusions:

  • The modified FDM offers a straightforward approach to studying resonance phenomena.
  • This method allows for the incorporation of finite grid techniques in resonance calculations.
  • Potential applications include calculating electronic autoionization and nuclear predissociation resonances.