Minimum number-phase uncertainty states via weighted Bergman spaces

TL;DR

This paper extends Luo's number-phase uncertainty results from Hardy spaces to weighted Bergman spaces, explicitly identifying the states that minimize the uncertainty, thereby broadening the mathematical framework for quantum uncertainty analysis.

Contribution

It introduces a generalization of minimum uncertainty states from Hardy to weighted Bergman spaces, providing explicit characterizations.

Findings

Extended Luo's uncertainty results to weighted Bergman spaces.

Explicitly identified minimum uncertainty states in the new setting.

Broadened the mathematical framework for quantum uncertainty analysis.

Abstract

The number-phase uncertainty result of Luo via the Hardy space on unit disc (Phys Lett A, 2000) is extended in this paper to the scale of weighted Bergman spaces. The minimum uncertainty states are thereby explicitly identified.