论文标题
特征状态的力矩和饱和特性
Moments and saturation properties of eigenstates
论文作者
论文摘要
特征值是针对可观察到的代数的任何元素定义的，并且不需要在波函数或密度矩阵方面表示。此处为谐波振荡器提供了基于矩的系统代数派生，以及对鼻系统的扰动处理。在此过程中，发现了一系列不平等现象，这相当于谐波振荡器激发态饱和的高阶矩的不确定性关系。通过扰动理论中的顺序，Anharmonic Systems Order的类似饱和属性。因此，基于状态瞬间的复发关系与积极条件相结合的新方法可以显示新的物理特征。
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.
