Spherical harmonics in p dimensions /
Efthimiou, Costas,
Spherical harmonics in p dimensions / Costas Efthimiou, Christopher Frye. - 1 online resource (xii, 143 pages) : illustrations
Includes bibliographical references and index.
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.
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 calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter.
English.
9789814596701 (electronic bk.) 9814596701 (electronic bk.) 1322030723 (ebk) 9781322030722 (ebk)
634323 MIL
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.
Electronic books.
QC20.7.S645 / E38 2014eb
515/.785
Spherical harmonics in p dimensions / Costas Efthimiou, Christopher Frye. - 1 online resource (xii, 143 pages) : illustrations
Includes bibliographical references and index.
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.
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 calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter.
English.
9789814596701 (electronic bk.) 9814596701 (electronic bk.) 1322030723 (ebk) 9781322030722 (ebk)
634323 MIL
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.
Electronic books.
QC20.7.S645 / E38 2014eb
515/.785