This note proves that the annihilation operator of a quantum harmonic oscillator admits an invariant distributionally -scrambled linear manifold for any . This is a positive answer to Question 1 by Wu and Chen (2013).
Xinxing Wu. "Invariant Distributionally Scrambled Manifolds for an Annihilation Operator." Abstr. Appl. Anal. 2014 (SI20) 1 - 4, 2014. https://doi.org/10.1155/2014/754960