theorem 9.78 Semiclassical quantisation of a well

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2888 · p. 306

Rests on

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 ¶

Supports

depends_on example 9.80 The 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 52.24 The p-mode cavity ¶
- depends_on phenomenon 52.25 The Sun rings, and its interior can be inverted ¶
  - depends_on phenomenon 52.22 The solar-neutrino deficit, and its resolution ¶

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`	→	The semiclassical wave	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2904
`depends_on`	→	eq:slt-wkb-schrodinger	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2904
`depends_on`	→	Connection formulae	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2904
`depends_on`	←	The harmonic oscillator	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2988
`depends_on`	←	Bohr–Sommerfeld and Einstein–Brillouin–Keller quantization	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1186
`depends_on`	←	The p-mode cavity	declared	parts/05-general-relativity-cosmology/11-stellar-structure-nucleosynthesis.tex:1883
`proves`	←	ch:07-odes-sturm-liouville@proof-40	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2907