proposition 23.38 Bohr–Sommerfeld and Einstein–Brillouin–Keller quantization

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:1167 · p. 837

Rests on

depends_on definition 23.28 Action variables ¶
- depends_on definition 16.99 Abbreviated action ¶
  - depends_on definition 16.96 Action; Hamilton's principle ¶
    - depends_on definition 21.31 Lagrangian ¶
    - depends_on equation 16.11 eq:calcvar-basic-functional ¶
  - depends_on equation 16.86 eq:calcvar-hamilton-action ¶
- depends_on definition 23.13 Additive separability ¶
  - depends_on definition 23.5 Complete integral ¶
    - depends_on equation 23.2 eq:hj-equation ¶
  - depends_on equation 23.15 eq:hj-characteristic-equation ¶
depends_on remark 9.79 Where the one half comes from ¶
depends_on theorem 9.78 Semiclassical quantisation of a well ¶
- depends_on corollary 9.62 The semiclassical wave ¶
  - depends_on equation 9.62 eq:slt-wkb-ansatz ¶
  - depends_on equation 9.61 eq:slt-wkb-kappa ¶
  - depends_on proposition 9.61 Eikonal and transport equations ¶
    - depends_on equation 9.64 eq:slt-wkb-series ¶
    - depends_on proposition 9.60 Exact Riccati form ¶
      - depends_on equation 9.62 eq:slt-wkb-ansatz ¶ ↺
      - depends_on equation 9.60 eq:slt-wkb-normal-form ¶
      - proves proof ch:07-odes-sturm-liouville@proof-30 ¶
    - proves proof ch:07-odes-sturm-liouville@proof-31 ¶
  - proves proof ch:07-odes-sturm-liouville@proof-32 ¶
- depends_on equation 9.59 eq:slt-wkb-schrodinger ¶
- depends_on theorem 9.72 Connection formulae ¶
  - depends_on corollary 9.62 The semiclassical wave ¶ ↺
  - depends_on equation 9.79 eq:slt-wkb-airy-ai ¶
  - depends_on equation 9.80 eq:slt-wkb-airy-bi ¶
  - depends_on equation 9.76 eq:slt-wkb-airy-equation ¶
  - depends_on equation 9.74 eq:slt-wkb-airy-scale ¶
  - proves proof ch:07-odes-sturm-liouville@proof-37 ¶
- proves proof ch:07-odes-sturm-liouville@proof-40 ¶
proves proof ch:06-hamilton-jacobi@proof-10 ¶

Supports

depends_on remark 24.57 The half-integer, and the honest status of the construction ¶

Neighborhood

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Edges

type	direction	node	provenance	where
`cites` (history)	→	Zur Quantentheorie der Spektrallinien	derived	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1176
`depends_on`	→	Action variables	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1186
`depends_on`	→	Where the one half comes from	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1186
`depends_on`	→	Semiclassical quantisation of a well	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1186
`depends_on`	←	The half-integer, and the honest status of the construction	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1979
`proves`	←	ch:06-hamilton-jacobi@proof-10	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1190