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arXiv · 2012.10321

Moments and saturation properties of eigenstates

Martin Bojowald·Jonathan Guglielmon·Martijn van Kuppeveld
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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.

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Martin Bojowald, Jonathan Guglielmon, Martijn van Kuppeveld. 2020-12-18. Moments and saturation properties of eigenstates. https://doi.org/10.1103/physrevd.103.126005

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