Quasidecay of harmonic oscillator coherent states in nonharmonic potentials

Abstract

The time evolution of harmonic oscillator coherent states (HOCS’s) (displaced ground state wave functions) in symmetrical and nonsymmetrical nonharmonic potentials is studied numerically. The potentials were modeled with an ansatz V(ε, q) = (1−ε) VHO+ε VNH, where VHO is the harmonic oscillator potential and VNH is chosen as a convenient Morse oscillator (nonsymmetrical) or as a negative Gaussian (symmetrical) so that the potential near the minimum is not distorted. The initially well located HOCS’s decay within a medium time scale of 5–100 classical oscillations to a wave packet which is delocalized in the position area of the potential well between the classical turning points. The time period up to this delocalization is designed as quasidecay time τQ, and it is demonstrated with some examples that in the symmetrical potentials the HOCS is refocused after a period of τR = 8τQ, while, as a rule, in the nonsymmetrical potential the recurrences need much longer time and could not be observed in the time scale under investigation. It is shown that the absolute values of the quasidecay times cannot be related either to the energy moments 〈H〉 and ΔH nor to the contribution of a quasicontinuum to the initial HOCS but that there is a strong correlation of ΔH and τQ for the nonsymmetrical potential considering only initial wave packets of the same energy.