theorem 9.76 Semiclassical transmission through a barrier

open in the book · parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2759 · p. 304

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 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

assumes experiment Cockcroft and Walton: lithium split by accelerated protons ¶
- cites (data) derived bib 3261 Disintegration of Lithium by Swift Protons ¶
- cites (evidence) derived bib 3261 Disintegration of Lithium by Swift Protons ¶ ↺
- cites (method) derived bib 830 Experiments with high velocity positive ions.---(I) Further developments in the method of obtaining high velocity positive ions ¶
- cites (data) derived bib 831 Experiments with high velocity positive ions. II. -The disintegration of elements by high velocity protons ¶
- cites (data) derived bib 831 Experiments with high velocity positive ions. II. -The disintegration of elements by high velocity protons ¶ ↺
- cites (evidence) derived bib 831 Experiments with high velocity positive ions. II. -The disintegration of elements by high velocity protons ¶ ↺
- cites (context) derived bib 3-4 Zur Quantentheorie des Atomkernes ¶
- cites (context) derived bib 3-4 Zur Quantentheorie des Atomkernes ¶ ↺
- cites (context) derived bib 3073 Wave Mechanics and Radioactive Disintegration ¶
- cites (context) derived bib 3073 Wave Mechanics and Radioactive Disintegration ¶ ↺
- cites (context) derived bib 2 Quantum Mechanics and Radioactive Disintegration ¶
- cites (context) derived bib 2 Quantum Mechanics and Radioactive Disintegration ¶ ↺
- … 1 more
depends_on example 9.81 Gamow factor for an alpha particle, in SI ¶
- depends_on example 9.82 Checking the validity criterion for the barrier above ¶
depends_on phenomenon 117.5 The reaction proceeds far below the Coulomb barrier ¶
- tests experiment Cockcroft and Walton: lithium split by accelerated protons ¶ ↺
depends_on theorem 107.63 Alpha decay rate ¶

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:2783
`depends_on`	→	The transport equation is flux conservation	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2783
`depends_on`	→	Connection formulae	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2783
`assumes`	←	Cockcroft and Walton: lithium split by accelerated protons	declared	parts/11-qft-standard-model/19-exp-nuclear-transmutation.tex:542
`depends_on`	←	Gamow factor for an alpha particle, in SI	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3075
`depends_on`	←	The reaction proceeds far below the Coulomb barrier	declared	parts/11-qft-standard-model/19-exp-nuclear-transmutation.tex:905
`depends_on`	←	Alpha decay rate	declared	parts/11-qft-standard-model/09-nuclear-physics.tex:2637
`proves`	←	ch:07-odes-sturm-liouville@proof-39	declared	parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2785