spherical coordinates
♦
9 matching pages ♦
(0.001 seconds)
9 matching pages
1: 14.31 Other Applications
…
►Many additional physical applications of Legendre polynomials and associated Legendre functions include solution of the Helmholtz equation, as well as the Laplace equation, in spherical coordinates (Temme (1996b)), quantum mechanics (Edmonds (1974)), and high-frequency scattering by a sphere (Nussenzveig (1965)).
…
2: 14.30 Spherical and Spheroidal Harmonics
…
►As an example, Laplace’s equation in spherical coordinates (§1.5(ii)):
…
►Here, in spherical coordinates, is the squared angular momentum operator:
…
3: 1.5 Calculus of Two or More Variables
4: 18.39 Physical Applications
5: 10.73 Physical Applications
…
►The functions , , , and arise in the solution (again by separation of variables) of the Helmholtz equation in spherical coordinates
(§1.5(ii)):
…
6: 31.10 Integral Equations and Representations
7: 29.18 Mathematical Applications
…
►
§29.18(i) Sphero-Conal Coordinates
… ►when transformed to sphero-conal coordinates : … ►§29.18(ii) Ellipsoidal Coordinates
►The wave equation (29.18.1), when transformed to ellipsoidal coordinates : … ►§29.18(iii) Spherical and Ellipsoidal Harmonics
…8: 30.2 Differential Equations
…
►In applications involving prolate spheroidal coordinates
is positive, in applications involving oblate spheroidal coordinates
is negative; see §§30.13, 30.14.
…
►If , Equation (30.2.4) is satisfied by spherical Bessel functions; see (10.47.1).