We develop a series solution for the bound-state energy levels of the quantum-mechanical one-dimensional finite square-well potential. We show that this general solution is useful for local approximations of the energy spectrum (which target a particular energy range of the potential well for high accuracy), for global approximations of the energy spectrum (which provide analytic expressions of reasonable accuracy for the entire range of bound states), and for numerical methods. This solution also provides an analytic description of dynamical phenomena; with it, we compute the time scales of classical motion, revivals, and super-revivals for wave-packet states excited in the well.We develop a series solution for the bound-state energy levels of the quantum-mechanical one-dimensional finite square-well potential. We show that this general solution is useful for local approximations of the energy spectrum (which target a particular energy range of the potential well for high accuracy), for global approximations of the energy spectrum (which provide analytic expressions of reasonable accuracy for the entire range of bound states), and for numerical methods. This solution also provides an analytic description of dynamical phenomena; with it, we compute the time scales of classical motion, revivals, and super-revivals for wave-packet states excited in the well.

American Journal of PhysicsOct 1, 200040 citations

Impossibility of simultaneous localization of wave packets in energy and in configuration space

Werner O. Amrein, Anne Boutet de Monvel-Berthier

Reports on Mathematical PhysicsFeb 1, 19771 citation

Revivals of wave packets: General theory and application to Rydberg clusters

O. Knospe, R. Schmidt

A universal approach is developed to study revivals of wave packets made of bound states with an arbitrary spectrum ${\mathit{E}}_{\mathit{n}}$ exhibiting hierarchical time scales. An analytic expression in form of a recursion formula is derived, which allows for a given wave packet the prediction of all revival times in any time scale. The theory is applied to metallic Rydberg clusters, i.e., two oppositely charged metallic clusters in a bound state with high angular momentum, taking into account their mutual polarization connected with a complicated n dependence of the spectrum ${\mathit{E}}_{\mathit{n}}$ . The theoretical predictions are compared with numerical results using a stroboscopic picture of the autocorrelation function. \textcopyright{} 1996 The American Physical Society.A universal approach is developed to study revivals of wave packets made of bound states with an arbitrary spectrum ${\mathit{E}}_{\mathit{n}}$ exhibiting hierarchical time scales. An analytic expression in form of a recursion formula is derived, which allows for a given wave packet the prediction of all revival times in any time scale. The theory is applied to metallic Rydberg clusters, i.e., two oppositely charged metallic clusters in a bound state with high angular momentum, taking into account their mutual polarization connected with a complicated n dependence of the spectrum ${\mathit{E}}_{\mathit{n}}$. The theoretical predictions are compared with numerical results using a stroboscopic picture of the autocorrelation function. \textcopyright{} 1996 The American Physical Society.

Physical Review AAug 1, 199638 citations

Revival Times for a Generalized Coherent State

Katherine Newton, Micheal S. Berger

Bulletin of the American Physical SocietyOct 29, 20150 citations

A universal approach is developed to study revivals of wave packets made of bound states with an arbitrary spectrum

{\mathit{E}}_{\mathit{n}}

exhibiting hierarchical time scales. An analytic expression in form of a recursion formula is derived, which allows for a given wave packet the prediction of all revival times in any time scale. The theory is applied to metallic Rydberg clusters, i.e., two oppositely charged metallic clusters in a bound state with high angular momentum, taking into account their mutual polarization connected with a complicated n dependence of the spectrum

{\mathit{E}}_{\mathit{n}}

. The theoretical predictions are compared with numerical results using a stroboscopic picture of the autocorrelation function. \textcopyright{} 1996 The American Physical Society.