Wu, Xinxing; Zhu, Peiyong The principal measure of a quantum harmonic oscillator. (English) Zbl 1238.81129 J. Phys. A, Math. Theor. 44, No. 50, Article ID 505101, 6 p. (2011). Summary: At the end of his paper [P. Oprocha, J. Phys. A, Math. Gen. 39, No. 47, 14559–14565 (2006; Zbl 1107.81026)], Oprocha said that it is difficult and interesting to know the exact value of the principal measure of an annihilation operator \(\widetilde a\) of the unforced quantum harmonic oscillator. Motivated by this, in this paper, we prove that this exact value is equal to 1. Besides, we point out that \(\widetilde a\) exhibits distributional \(\epsilon\)-chaos for any \(0 < \epsilon < 2\). Cited in 1 ReviewCited in 10 Documents MSC: 81Q50 Quantum chaos Citations:Zbl 1107.81026 PDFBibTeX XMLCite \textit{X. Wu} and \textit{P. Zhu}, J. Phys. A, Math. Theor. 44, No. 50, Article ID 505101, 6 p. (2011; Zbl 1238.81129) Full Text: DOI