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The principal measure of a quantum harmonic oscillator. (English) Zbl 1238.81129

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 \(0 < \epsilon < 2\).

MSC:

81Q50 Quantum chaos

Citations:

Zbl 1107.81026
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