Analytical expressions on harmonic oscillators for variational path integrals

Abstract

In this study, we derive analytical expressions for one-dimensional harmonic oscillators for variational path integrals (VPIs). A Gaussian-type trial wavefunction is adopted. Total and potential energies of the system are analytically expressed both for the continuous time and an approximate discretised VPIs. Obtained expressions are numerically verified using molecular dynamics calculations. Convergence properties regarding the projection time and the Trotter number are discussed.

Keywords::

• quantum Monte Carlo
• variational path integral
• molecular dynamics
• harmonic oscillator

Acknowledgements

This work was partially supported by the Grant-in-Aid for Scientific Research (C) (No. 23550011) from the Japan Society for the Promotion of Science and by the Strategic Programs for Innovative Research (SPIRE), MEXT and the Computational Materials Science Initiative (CMSI), Japan.

Notes

^1. Email: [email protected]