标题： 矩和本征态的饱和性质 显示英文标题

标题： Moments and saturation properties of eigenstates

摘要： 特征值对于可观测代数中的任何元素都定义，并不需要用波函数或密度矩阵来表示。 这里基于矩量进行系统的代数推导，针对简谐振子进行了阐述，并对非简谐系统进行了微扰处理。 在此过程中，发现了一组不等式，这些不等式相当于由简谐振子激发态饱和的高阶矩的不确定性关系。 类似的饱和性质在微扰理论中按顺序适用于非简谐系统。 因此，基于状态矩的递推关系与正定条件的新方法能够展示新的物理特性。 显示英文摘要

摘要： Eigenvalues are defined for any element of an algebra of observables and do not require a representation in terms of wave functions or density matrices. A systematic algebraic derivation based on moments is presented here for the harmonic oscillator, together with a perturbative treatment of anharmonic systems. In this process, a collection of inequalities is uncovered which amount to uncertainty relations for higher-order moments saturated by the harmonic-oscillator excited states. Similar saturation properties hold for anharmonic systems order by order in perturbation theory. The new method, based on recurrence relations for moments of a state combined with positivity conditions, is therefore able to show new physical features.