Validity of the time-dependent variational approximation to the Gaussian wavepacket method applied to double-well systems

TL;DR

This study evaluates the accuracy of the time-dependent variational approximation to the Gaussian wavepacket method in double-well quantum systems, revealing limitations due to wavepacket deformation and questioning its applicability.

Contribution

The paper critically assesses the validity of TDVA for double-well systems by comparing it with quasi-exact spectral method results, highlighting its limitations.

Findings

Wavepackets deform quickly in double-well systems.

TDVA assumptions on higher-order fluctuations are unjustified.

Results cast doubt on TDVA's applicability to double-well systems.

Abstract

We have examined the validity of the time-dependent variational approximation (TDVA) to the Gaussian wavepacket method (GWM) for quantum double-well (DW) systems, by using the quasi-exact spectral method (SM). Comparisons between results of wavefunctions, averages of position and momentum, the auto-correlation function, and an uncertainty product calculated by SM and TDVA have been made. It has been shown that a given initial Gaussian wavepacket in SM is quickly deformed at $t > 0$ where a wavepacket cannot be expressed by a {\it single} Gaussian, and that assumptions on averages of higher-order fluctuations in TDVA are not justified. These results cast some doubt on an application of TDVA to DW systems. Gaussian wavepacket dynamics in anharmonic potential systems is studied also.