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• W3116905657 abstract "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." @default.
• W3116905657 created "2021-01-05" @default.
• W3116905657 creator A5045617442 @default.
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• W3116905657 date "2020-12-18" @default.
• W3116905657 modified "2023-09-27" @default.
• W3116905657 title "Moments and saturation properties of eigenstates" @default.
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• W3116905657 hasPublicationYear "2020" @default.
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