Non-integrability of the 3-D hydrogen atom under motional Stark effect or circularly polarized microwave combined with magnetic fields
✍ Scribed by Sebastián Ferrer; Félix Mondéjar
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 101 KB
- Volume
- 264
- Category
- Article
- ISSN
- 0375-9601
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✦ Synopsis
Limits of the motional Stark effect on Rydberg atoms under the crossed magnetic and electric fields in the case of identical masses, and the hydrogen atom with combined circularly polarized microwave field and a magnetic field that is perpendicular to the plane of polarization have been shown recently to be integrable in the manifold z s Z s 0. In this letter we prove the non integrability, in the Liouville-Arnold sense, of the Hamiltonian system corresponding to those limits in 3-dimensions. The proof makes use of a theorem of Morales and Ramis about non integrability based on differential Galois theory.