Eigenstate
An eigenstate is a quantum state that has a definite value of a particular Observable, meaning a measurement of that observable is certain to return one specific result. That result is the eigenvalue associated with the eigenstate, and the two are linked by the eigenvalue equation for the operator representing the observable.
Measurement and collapse
Most quantum states are not eigenstates of a given observable; they are superpositions of several eigenstates, so the measurement outcome is probabilistic. According to the standard account of measurement, observing the quantity leaves the system in one eigenstate of that observable, and the value obtained is the corresponding eigenvalue. Which outcome occurs is random, with probabilities set by the state beforehand. The physical status of this jump lies at the heart of the measurement problem. Compatible observables can share a common set of eigenstates.
Sources
- Quantum Mechanics (Stanford Encyclopedia of Philosophy) (Stanford Encyclopedia of Philosophy, 2021)
- Measurement in Quantum Theory (Stanford Encyclopedia of Philosophy) (Stanford Encyclopedia of Philosophy, 2021)
Cite this entry
"Eigenstate." postquantum.wiki. Updated July 11, 2026. https://postquantum.wiki/eigenstate@misc{pqwiki-eigenstate,
title = {Eigenstate},
howpublished = {\url{https://postquantum.wiki/eigenstate}},
year = {2026},
note = {postquantum.wiki, updated 2026-07-11}
}