Note on «Quantum harmonic oscillator in a strong electrostatic wave»
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We discuss the validity criteria of the approximation used in M. Frasca:Nuovo Cimento B,107, 845 (1992), to study a quantum harmonic oscillator in a plane wave of large amplitude. It is shown that the ratio between the frequency of the oscillator and that of the wave must be an irrational number. This result is obtained by computing the first correction to the leading order of the strong-field approximation. As in the cited paper, we assume that the wave begins acting on the particle in the far past. By this calculation we support the result that there exists a small but finite probability to have transitions of the oscillator to very high-energy states.
PACS06.65 Quantum theory quantum mechanics
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