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Helmholtz equation


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1: 34.12 Physical Applications
§34.12 Physical Applications
3 j , 6 j , and 9 j symbols are also found in multipole expansions of solutions of the Laplace and Helmholtz equations; see Carlson and Rushbrooke (1950) and Judd (1976).
2: 10.73 Physical Applications
The Helmholtz equation, ( 2 + k 2 ) ψ = 0 , follows from the wave equation … …
§10.73(ii) Spherical Bessel Functions
3: 14.31 Other Applications
§14.31(iii) Miscellaneous
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)). …
4: 12.17 Physical Applications
§12.17 Physical Applications
The main applications of PCFs in mathematical physics arise when solving the Helmholtz equationIn a similar manner coordinates of the paraboloid of revolution transform the Helmholtz equation into equations related to the differential equations considered in this chapter. …
5: 28.32 Mathematical Applications
§28.32(ii) Paraboloidal Coordinates
When the Helmholtz equation