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Updated: Jun 23, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Recursive Schrödinger equation approach to faster converging path integrals.

Antun Balaz¹, Aleksandar Bogojević, Ivana Vidanović

¹Scientific Computing Laboratory, Institute of Physics Belgrade, Pregrevica 118, 11080 Belgrade, Serbia. antun@phy.bg.ac.yu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 28, 2009

Summary

Researchers developed a systematic method to derive analytic expressions for discretized effective actions by solving the Schrödinger equation. This advances quantum system analysis and speeds up numerical calculations.

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Area of Science:

Quantum mechanics
Computational physics

Background:

Path integral Monte Carlo methods are crucial for quantum system simulations.
Deriving accurate effective actions and propagators is computationally intensive.
Existing methods have limitations in achievable orders of accuracy.

Purpose of the Study:

To develop an efficient, systematic approach for deriving analytic expressions of discretized effective actions.
To obtain high-order discrete short-time propagators for quantum systems.
To enhance the speed and applicability of numerical and analytical methods in quantum mechanics.

Main Methods:

Recursive solution of the Schrödinger equation.
Derivation of analytic expressions for discretized effective actions.
Calculation of discrete short-time propagators in arbitrary dimensions.

Main Results:

An efficient, systematic approach for deriving analytic expressions for discretized effective actions.
High-order discrete short-time propagators for one- and many-particle systems.
Demonstrated applicability to accelerate Monte Carlo path integral calculations.

Conclusions:

The new method provides accurate, high-order propagators.
This approach offers a significant speedup for numerical simulations.
It enables alternative analytical approximation schemes for quantum system properties.