equation 23.2 eq:hj-equation

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Supports

• depends_on definition 23.5 Complete integral ¶
  • depends_on definition 23.52 Lagrangian family; caustic ¶
    • depends_on proposition 23.54 The geometrical amplitude diverges ¶
      • depends_on proposition 23.55 The fold, and the quarter-power law ¶
        • depends_on proposition 23.56 The phase jump at a fold ¶
        • depends_on remark 23.58 The caustics that are not turning surfaces ¶
      • depends_on remark 23.59 What is observed ¶
    • depends_on proposition 23.53 A caustic point is a conjugate point ¶
  • 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 theorem 23.31 Liouville–Arnold ¶
      • 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 23.6 Jacobi ¶
    • depends_on example 23.25 Central force in plane polar coordinates ¶ ↺
    • depends_on example 23.22 Free particle ¶ ↺
    • depends_on example 23.23 Uniform gravity, and the parabola ¶ ↺
    • depends_on proposition 23.7 The principal function is the action ¶
      • depends_on remark 23.8 The action as a function, not a functional ¶
• depends_on proposition 23.44 Relativistic Hamilton–Jacobi equation ¶
  • depends_on remark 23.46 Carter's constant ¶
  • depends_on remark 23.45 Why this is not an analogy ¶
• depends_on proposition 23.9 Separation of the time ¶
  • depends_on proposition 23.10 The characteristic function is the abbreviated action ¶
    • depends_on remark 23.11 Whose principle, and where it fails ¶
  • depends_on remark 23.12 Two functions, two roles ¶
• depends_on proposition 23.47 The Hamilton–Jacobi equation as the classical limit ¶
• depends_on remark 23.3 What Part II owes this chapter ¶
• depends_on remark 23.4 What the equation costs and what it buys ¶
• step_from equation 23.13 eq:hj-dsdt-chain ¶