Moments and saturation properties of eigenstates: Oscillator systems

Martin Bojowald, Jonathan Guglielmon, Martijn Van Kuppeveld

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number126005
JournalPhysical Review D
Volume103
Issue number12
DOIs
StatePublished - Jun 15 2021

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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