caa a22 4500 605487162 CHVBK 20210128100449.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00214-014-1592-4 doi (NATIONALLICENCE)springer-10.1007/s00214-014-1592-4 Semiclassical quantization of atomic systems through their normal form: the hydrogen atom [Elektronische Daten] [Charles Jaffé, Jesús Palacián, Patricia Yanguas, T. Uzer] Over a century after Bohr's the initial quantization of hydrogen, the semiclassical quantization of atomic systems still represents a challenge. In the present paper, we re-examine the semiclassical quantization of hydrogen asking the question: How can hydrogen be quantized without making use of its separability? The approach adopted was to explicitly a construct transformation from the physical variable to the action-angle variables. The initial difficulty encountered is the lack of an equilibrium point on the potential energy surface. To surmount this difficulty, it is noted that the circular periodic orbits are relative equilibria. In a rotating frame, the relative equilibria become critical points in the phase flow. It is shown that the flow in the vicinity of the critical point is stable. The Lie-Deprit transformation is then used to transform the system into normal form, following which the semiclassical quantization is straightforward. Springer-Verlag Berlin Heidelberg, 2014 Semiclassical quantization nationallicence Hydrogen nationallicence Normal form nationallicence Canonical transformation nationallicence Relative equilibria nationallicence Rotating frame nationallicence Jaffé Charles Department of Chemistry, West Virginia University, 26506-6045, Morgantown, WV, USA aut Palacián Jesús Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 3100, Pamplona, Spain aut Yanguas Patricia Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 3100, Pamplona, Spain aut Uzer T. Center for Nonlinear Sciences, School of Physics, Georgia Institute of Technology, 30332-0430, Atlanta, GA, USA aut Theoretical Chemistry Accounts Springer Berlin Heidelberg 134/1(2015-01-01), 1-7 1432-881X 134:1<1 2015 134 214 https://doi.org/10.1007/s00214-014-1592-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00214-014-1592-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jaffé Charles Department of Chemistry, West Virginia University, 26506-6045, Morgantown, WV, USA aut NATIONALLICENCE 700 1- Palacián Jesús Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 3100, Pamplona, Spain aut NATIONALLICENCE 700 1- Yanguas Patricia Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 3100, Pamplona, Spain aut NATIONALLICENCE 700 1- Uzer T. Center for Nonlinear Sciences, School of Physics, Georgia Institute of Technology, 30332-0430, Atlanta, GA, USA aut NATIONALLICENCE 773 0- Theoretical Chemistry Accounts Springer Berlin Heidelberg 134/1(2015-01-01), 1-7 1432-881X 134:1<1 2015 134 214