Uncertainty principles for the imaginary Ornstein-Uhlenbeck operator

TL;DR

This paper establishes uncertainty principles for the Schrödinger group associated with the Ornstein-Uhlenbeck operator, leading to equivalent results for the imaginary harmonic oscillator, advancing understanding of quantum uncertainty in these contexts.

Contribution

It introduces new uncertainty principles specifically for the Schrödinger group generated by the Ornstein-Uhlenbeck operator and connects these to the imaginary harmonic oscillator.

Findings

Proves two forms of uncertainty principles for the Ornstein-Uhlenbeck operator.

Derives an equivalent uncertainty result for the imaginary harmonic oscillator.

Enhances theoretical understanding of quantum operators and their uncertainty properties.

Abstract

We prove two forms of uncertainty principle for the Schr\"odinger group generated by the Ornstein-Uhlenbeck operator. As a consequence, we derive a related (in fact, equivalent) result for the imaginary harmonic oscillator.