Stability of Quantum Harmonic Oscillator under Time Quasi-periodic Perturbation
نویسندگان
چکیده
— We prove stability of the bound states for the quantum harmonic oscillator under non-resonant, time quasi-periodic perturbations by proving that the associated Floquet Hamiltonian has pure point spectrum. Résumé (Stabilité de l’oscillateur harmonique quantique sous les perturbations quasipériodiques) Nous démontrons la stabilité des états bornés de l’oscillateur harmonique sous les perturbations non-résonantes, quasi-périodiques en temps en démontrant que l’hamiltonien Floquet associé a un spectre purement ponctuel. The stability of the quantum harmonic oscillator is a long standing problem since the establishment of quantum mechanics. The Schrödinger equation for the harmonic oscillator in R (in appropriate coordinates) is the following: (1) −i ∂ ∂t ψ = 1 2 n
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