Moments and saturation properties of eigenstates
- URL: http://arxiv.org/abs/2012.10321v1
- Date: Fri, 18 Dec 2020 16:05:17 GMT
- Title: Moments and saturation properties of eigenstates
- Authors: Martin Bojowald, Jonathan Guglielmon and Martijn van Kuppeveld
- Abstract summary: 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 collection of inequalities is uncovered which amount to uncertainty relations for higher-order moments saturated by the harmonic-oscillator excited states.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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