Semiclassical quantization of atomic systems through their normal form: the hydrogen atom
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| 024 | 7 | 0 | |a 10.1007/s00214-014-1592-4 |2 doi |
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| 245 | 0 | 0 | |a Semiclassical quantization of atomic systems through their normal form: the hydrogen atom |h [Elektronische Daten] |c [Charles Jaffé, Jesús Palacián, Patricia Yanguas, T. Uzer] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Semiclassical quantization |2 nationallicence | |
| 690 | 7 | |a Hydrogen |2 nationallicence | |
| 690 | 7 | |a Normal form |2 nationallicence | |
| 690 | 7 | |a Canonical transformation |2 nationallicence | |
| 690 | 7 | |a Relative equilibria |2 nationallicence | |
| 690 | 7 | |a Rotating frame |2 nationallicence | |
| 700 | 1 | |a Jaffé |D Charles |u Department of Chemistry, West Virginia University, 26506-6045, Morgantown, WV, USA |4 aut | |
| 700 | 1 | |a Palacián |D Jesús |u Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 3100, Pamplona, Spain |4 aut | |
| 700 | 1 | |a Yanguas |D Patricia |u Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 3100, Pamplona, Spain |4 aut | |
| 700 | 1 | |a Uzer |D T. |u Center for Nonlinear Sciences, School of Physics, Georgia Institute of Technology, 30332-0430, Atlanta, GA, USA |4 aut | |
| 773 | 0 | |t Theoretical Chemistry Accounts |d Springer Berlin Heidelberg |g 134/1(2015-01-01), 1-7 |x 1432-881X |q 134:1<1 |1 2015 |2 134 |o 214 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00214-014-1592-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00214-014-1592-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Jaffé |D Charles |u Department of Chemistry, West Virginia University, 26506-6045, Morgantown, WV, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Palacián |D Jesús |u Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 3100, Pamplona, Spain |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Yanguas |D Patricia |u Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 3100, Pamplona, Spain |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Uzer |D T. |u Center for Nonlinear Sciences, School of Physics, Georgia Institute of Technology, 30332-0430, Atlanta, GA, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Theoretical Chemistry Accounts |d Springer Berlin Heidelberg |g 134/1(2015-01-01), 1-7 |x 1432-881X |q 134:1<1 |1 2015 |2 134 |o 214 | ||