example 9.81 Gamow factor for an alpha particle, in SI

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2994 · p. 307

example -- no derivation owed by its kind

Rests on

depends_on theorem 9.76 Semiclassical transmission through a barrier ¶
- 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 proposition 9.63 The transport equation is flux conservation ¶
  - depends_on corollary 9.62 The semiclassical wave ¶ ↺
  - proves proof ch:07-odes-sturm-liouville@proof-33 ¶
- 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-39 ¶

Supports

depends_on example 9.82 Checking the validity criterion for the barrier above ¶

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
`cites`	→	CODATA recommended values of the fundamental physical constants: 2018	derived	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3004
`cites`	→	CODATA recommended values of the fundamental physical constants: 2018	derived	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3005
`depends_on`	→	Semiclassical transmission through a barrier	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3075
`depends_on`	←	Checking the validity criterion for the barrier above	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3103