1301.6423 (Hideo Hasegawa)

A comparison between Gaussian wavepacket dynamics of double-well systems
in the Schrödinger and Heisenberg approaches    [PDF]

Hideo Hasegawa

Detailed numerical studies on Gaussian wavepacket dynamics in quantum systems with symmetric and asymmetric double-well (DW) potentials have been made with the use of the two approaches: the Schr\"odinger approach (SA) and the Heisenberg approach combined with the time-dependent variational approximation (TDVA) to the Gaussian wavepacket method (GWM). We have calculated time dependences of wavefunctions, averages of position and momentum, the correlation function, an uncertainty product and the tunneling probability. Our calculations show that results of SA are rather different from those of TDVA-GWM: in particular, a given initial Gaussian wavepacket in SA is quickly deformed at $t > 0$ where a wavepacket cannot be expressed by a {\it single} Gaussian. These results cast some doubt on an application of TDVA-GWM to double-well systems.

View original: http://arxiv.org/abs/1301.6423