Metadata aliases: [Uncertainty in quantum mechanics] shorthands: {} created: 2021-12-11 12:52:02 modified: 2022-01-10 04:13:04 If is a self-adjoint operator on a Hilbert space and is a unit vector in , let denote the standard deviation associated with measurements of in the state , which is computed as
aliases: [Uncertainty in quantum mechanics] shorthands: {} created: 2021-12-11 12:52:02 modified: 2022-01-10 04:13:04
We refer to as the uncertainty of in the state .
For a single observable , it is possible to choose so that is as small as we like, but for two observables, if they do not commute, their uncertainties cannot be made arbitrarily small simultaneously.