proposition 9.65 Validity criterion
open in the book ·
parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2258
· p. 299
Rests on
-
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 ¶
Supports
- depends_on example 9.82 Checking the validity criterion for the barrier above ¶
-
depends_on
remark 23.51
Where the expansion breaks, and what is owed
¶
-
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 ¶
-
depends_on
proposition 23.57
The wave resolution at a turning surface
¶
- depends_on remark 23.50 The dictionary completed ¶
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 |
→ | Reduced de Broglie wavelength | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2268 |
depends_on |
→ | eq:slt-wkb-series | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2268 |
depends_on |
→ | Eikonal and transport equations | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2268 |
depends_on |
← | Checking the validity criterion for the barrier above | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:3103 |
depends_on |
← | Where the expansion breaks, and what is owed | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1762 |
depends_on |
← | The dictionary completed | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1735 |
proves |
← | ch:07-odes-sturm-liouville@proof-34 | declared | parts/02-mathematical-methods/07-odes-sturm-liouville.tex:2271 |