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arXiv:2102.12711 · Russian Physics Journal

Quantum States of the Kapitza Pendulum

Pavel A. Golovinski, Vladimir A. Dubinkin

Published May 1, 2022• 2 citations
arXivHTMLPDF
DOI
10.1007/s11182-022-02603-7

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The quantum states of the Kapitza pendulum are investigated within the framework of the effective potential obtained by the method of averaging over fast oscillations. An analytical estimate of the energy spectrum of stabilized states is given using a model potential. For the lowest states of the inverted pendulum, an expression is obtained for the spectrum in the form of the energies of a harmonic oscillator, refined according to the perturbation theory. Tunneling corrections to the energies of resonance states in two wells of the effective potential are found. The results of calculations of the structure of vibrational and rotational spectra of the Kapitza pendulum by the semiclassical method and by Numerov’s numerical algorithm are compared.
The quantum states of the Kapitza pendulum are investigated in the framework of the effective potential obtained by the method of averaging over fast oscillations. An analytical estimate of the energy spectrum of stabilized states is given using a model potential. For the lowest states of the inverted pendulum, an expression is obtained for the spectrum in the form of the energies of a harmonic oscillator, refined according to the perturbation theory. Tunneling corrections to the energies of resonance states in double-well effective potential are found. The results of calculations of the structure of vibrational and rotational spectra of the Kapitza pendulum by the semiclassical method and by the numerical Numerov’s algorithm are compared.