example 9.82 Checking the validity criterion for the barrier above

Rests on

• depends_on example 9.81 Gamow factor for an alpha particle, in SI ¶
  • 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 ¶
        • 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 ¶
• 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 ¶ ↺
  • proves proof ch:07-odes-sturm-liouville@proof-34 ¶

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