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Applying Bogomolny's quantization method to generic classical systems.

Kenneth G Kay1

  • 1Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel.

The Journal of Chemical Physics
|June 3, 2017
PubMed
Summary
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This study introduces a new method for calculating semiclassical energy levels using Bogomolny

Area of Science:

  • Quantum mechanics
  • Computational physics
  • Chemical physics

Background:

  • Bogomolny's quantization method offers semiclassical energy level estimates for bound states.
  • Calculating the energy-dependent transfer matrix (TE) is computationally intensive, limiting its application.
  • Existing methods require recalculating numerous classical trajectories for each energy level.

Purpose of the Study:

  • To develop novel initial value representation (IVR) formulas for the transfer matrix (TE).
  • To overcome computational limitations of Bogomolny's method for generic systems.
  • To enable accurate semiclassical energy level calculations for arbitrary systems.

Main Methods:

  • Generalizing the Herman-Kluk formula for the propagator.

Related Experiment Videos

  • Deriving semiclassical integral approximations for the Green's function.
  • Utilizing these approximations to construct the energy-dependent transfer matrix (TE).

    • Main Results:

    • Developed new IVR formulas for the transfer matrix (TE).
    • Demonstrated accurate semiclassical energy level calculations for 2D systems.
    • Showed that small transfer matrices yield precise results.

    Conclusions:

    • The new IVR formulas significantly enhance the applicability of Bogomolny's quantization method.
    • This approach provides an efficient and accurate pathway to semiclassical energy levels.
    • The method is suitable for generic systems lacking special classical scaling properties.