An Inventory of Uncertainty Relations

The Systematics of Uncertainty Principles

Uncertainty principles involve
  1. Transforms
  2. Uncertainty measures
  3. Uncertainty relations
  4. Minimum uncertain distributions
  5. Higher-order eigenmodes and generalized "M-squared" concepts
Let's take up each of these in turn.

Transforms

Uncertainty relations generally refer to relations between the uncertainties of transform pairs, i.e. functions or distributions that are related by some kind of transform relationship such a Fourier transform pair.
 

Uncertainty measures

 

Uncertainty relations

 

Minimum uncertainty distributions

Minimum uncertainty distributions are

Higher-order eigenmodes and generalized "M-squared" concepts