remark 23.51 Where the expansion breaks, and what is owed

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:1738 · p. 843

remark -- no derivation owed by its kind

Rests on

depends_on proposition 9.65 Validity criterion ¶
- depends_on definition 9.64 Reduced de Broglie wavelength ¶
  - depends_on equation 9.60 eq:slt-wkb-normal-form ¶
- depends_on equation 9.64 eq:slt-wkb-series ¶
- 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-34 ¶
depends_on theorem 9.72 Connection formulae ¶
- 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 ¶ ↺
  - proves proof ch:07-odes-sturm-liouville@proof-32 ¶
- 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 ¶

Supports

depends_on proposition 23.57 The wave resolution at a turning surface ¶
- depends_on remark 23.58 The caustics that are not turning surfaces ¶
- depends_on remark 23.59 What is observed ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Validity criterion	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1762
`depends_on`	→	Connection formulae	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1762
`depends_on`	←	The wave resolution at a turning surface	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1945