2000/02/29 by Dae-Yup Song · 40 citations
Mathematics · Physics and Astronomy · #Advanced Frequency and Time Standards #Anharmonicity #Compact operator #Computer science #Creation and annihilation operators #Geometry #Harmonic #Harmonic oscillator #Inverse #Ladder operator #Mathematical analysis #Mathematics #Operator (biology) #Parametric oscillator #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum harmonic oscillator #Quantum mechanics #Simple harmonic motion #Square (algebra) #Unitary state #Unitary transformation #quant-ph
paper · pdf · doi:10.1103/physreva.62.014103
published in Physical Review A 62(1) (American Physical Society) · Phys. Rev. A (Brief Report), in press
arxiv created 2000/04/18 · openalex publication_date 2000/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The unitary operator that transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different timescale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.