Spherical harmonics in p dimensions /

The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calc...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Efthimiou, Costas (Autor), Frye, Christopher (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, NJ : World Scientific, [2014]
Temas:
Spherical harmonics.
Spherical functions.
Legendre's polynomials.
Mathematical physics.
Harmoniques sphériques.
Fonctions sphériques.
Polynômes de Legendre.
Physique mathématique.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Legendre's polynomials
Mathematical physics
Spherical functions
Spherical harmonics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Introduction. 1.1. Separation of variables. 1.2. Quantum mechanical angular momentum
  • 2. Working in p dimensions. 2.1 Rotations in [symbol]. 2.2. Spherical coordinates in p dimensions. 2.3. The sphere in higher dimensions. 2.4. Arc length in spherical coordinates. 2.5. The divergence theorem in EP. 2.6. [symbol] in spherical coordinates. 2.7. Problems
  • 3. Orthogonal polymials. 3.1. Orthogonality and expansions. 3.2. The recurrence formula. 3.3. The Rodrigues formula. 3.4. Approximations by polynomials. 3.5. Hilbert space and completeness. 3.6. Problems
  • 4. Spherical harmonics in p dimensions. 4.1. Harmonic homogeneous polynomials. 4.2. Spherical harmonics and orthogonality. 4.3. Legendre polynomials. 4.4. Boundary value problems. 4.5. Problems
  • 5. Solutions to problems. 5.1. Solutions to problems of chapter 2. 5.2. Solutions to problems of chapter 3. 5.3. Solutions to problems of chapter 4.

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