lemma 10.28 The separation constant

open in the book · parts/02-mathematical-methods/08-pdes.tex:805 · p. 348

Rests on

depends_on definition A.118 Simple separation of the Helmholtz equation ¶
- depends_on theorem A.120 Stäckel and Robertson conditions ¶
  - depends_on example A.122 Cartesian ¶
  - depends_on example A.123 Circular cylindrical ¶
  - depends_on example A.124 Spherical ¶
  - depends_on proposition A.128 The ellipsoidal system separates ¶
    - depends_on proposition A.132 The count ¶
depends_on example 10.31 Cartesian separation ¶
- depends_on example A.122 Cartesian ¶ ↺
depends_on example 10.32 Cylindrical separation ¶
- depends_on example A.123 Circular cylindrical ¶ ↺
depends_on example 10.33 Spherical separation ¶
- depends_on example A.124 Spherical ¶ ↺
depends_on proposition 23.9 Separation of the time ¶
- depends_on proposition 23.10 The characteristic function is the abbreviated action ¶
  - depends_on remark 23.11 Whose principle, and where it fails ¶
- depends_on remark 23.12 Two functions, two roles ¶
depends_on proposition 10.29 Time separation reduces the canonical equations to Helmholtz ¶
- depends_on example 10.38 The vibrating string ¶
- depends_on phenomenon 28.53 Chladni's figures ¶
- depends_on theorem 10.36 Solution of the heat problem on an interval ¶
depends_on theorem 10.34 Separable systems for the Helmholtz operator ¶
- depends_on remark 23.19 The same conditions govern the Helmholtz equation ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Linear, semilinear, quasilinear	declared	parts/02-mathematical-methods/08-pdes.tex:810
`depends_on`	←	Simple separation of the Helmholtz equation	declared	appendices/A-long-proofs.tex:6781
`depends_on`	←	Cartesian separation	declared	parts/02-mathematical-methods/08-pdes.tex:891
`depends_on`	←	Cylindrical separation	declared	parts/02-mathematical-methods/08-pdes.tex:910
`depends_on`	←	Spherical separation	declared	parts/02-mathematical-methods/08-pdes.tex:940
`depends_on`	←	Separation of the time	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:315
`depends_on`	←	Time separation reduces the canonical equations to Helmholtz	declared	parts/02-mathematical-methods/08-pdes.tex:836
`depends_on`	←	Separable systems for the Helmholtz operator	declared	parts/02-mathematical-methods/08-pdes.tex:955
`proves`	←	ch:08-pdes@proof-9	declared	parts/02-mathematical-methods/08-pdes.tex:813