Mountain pass frozen planet orbits in the helium atom model
Preprint
Abstract
We seek frozen planet orbits for the helium atom through an application of the Mountain Pass Lemma to the Lagrangian action functional. Our method applies to a wide class of gravitational-like interaction potentials thus generalising the results in [7] (Cieliebak, Frauenfelder and Volkov - 2023). We also let the charge of the two electrons tend to zero and perform the asymptotic analysis to prove convergence to a limit trajectory having a collision-reflection singularity between the electrons.Keywords
All Related Versions
This publication has 8 references indexed in Scilit:
- Nondegeneracy and integral count of frozen planet orbits in heliumTunisian Journal of Mathematics, 2023
- Shooting for collinear periodic orbits in the Helium modelZeitschrift für angewandte Mathematik und Physik, 2023
- A variational approach to frozen planet orbits in heliumAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 2022
- On Langmuir’s periodic orbitArchiv der Mathematik, 2022
- Lagrangian relations and linear point billiardsNonlinearity, 2017
- Degenerate billiards in celestial mechanicsRegular and Chaotic Dynamics, 2017
- Closed orbits of fixed energy for singular Hamiltonian systemsArchive for Rational Mechanics and Analysis, 1990
- Solutions with minimal period for Hamiltonian systems in a potential wellAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 1987