equation 23.15 eq:hj-characteristic-equation

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Supports

• depends_on definition 23.13 Additive separability ¶
  • depends_on definition 23.28 Action variables ¶
    • depends_on example 23.24 Harmonic oscillator ¶
    • depends_on proposition 23.38 Bohr–Sommerfeld and Einstein–Brillouin–Keller quantization ¶
      • depends_on remark 24.57 The half-integer, and the honest status of the construction ¶
    • depends_on proposition 24.56 The Bohr–Sommerfeld condition is a triviality condition on the prequantum holonomy ¶
      • depends_on remark 24.57 The half-integer, and the honest status of the construction ¶ ↺
    • depends_on remark 23.29 Convention ¶
    • depends_on remark 29.45 What integrability buys, and where it stops ¶
    • depends_on theorem 23.30 Motion in action–angle variables ¶
      • depends_on example 23.24 Harmonic oscillator ¶ ↺
      • depends_on theorem 23.34 Adiabatic invariance of the action ¶
        • depends_on example 23.35 The slowly stiffened oscillator ¶
        • depends_on example 23.27 Charged particle in a uniform magnetic field ¶
        • depends_on remark 23.36 How good the invariance really is ¶
        • depends_on remark 23.37 Why this matters observationally ¶
      • depends_on theorem 23.31 Liouville–Arnold ¶
        • depends_on proposition 24.56 The Bohr–Sommerfeld condition is a triviality condition on the prequantum holonomy ¶ ↺
        • depends_on remark 23.33 Integrability is exceptional ¶
        • depends_on remark 23.32 What that proof imports ¶
        • depends_on theorem 32.51 Kolmogorov–Arnold–Moser, quoted ¶
        • depends_on theorem 32.47 Poincaré's non-integrability, quoted ¶
    • depends_on theorem 23.34 Adiabatic invariance of the action ¶ ↺
  • depends_on example 23.26 The Kepler problem, and the Bohr formula ¶
  • depends_on proposition 23.14 Cyclic coordinates ¶
    • depends_on example 23.25 Central force in plane polar coordinates ¶
    • depends_on example 23.22 Free particle ¶
      • depends_on remark 23.42 Phase speed and particle speed ¶
    • depends_on example 23.27 Charged particle in a uniform magnetic field ¶ ↺
    • depends_on example 23.23 Uniform gravity, and the parabola ¶
  • depends_on proposition 23.20 Separability implies integrability ¶
    • depends_on remark 23.21 The tensorial statement, and what Part II owes it ¶
    • depends_on remark 23.32 What that proof imports ¶ ↺
  • depends_on theorem 23.17 Stäckel's conditions are sufficient ¶
    • depends_on remark 23.18 The converse, and what this treatise does not prove ¶
    • depends_on remark 23.19 The same conditions govern the Helmholtz equation ¶
• depends_on theorem 23.17 Stäckel's conditions are sufficient ¶ ↺