Hyperspherical Harmonics

Name: Hyperspherical Harmonics
Brand: Springer Netherlands
SKU: 9789401075442
Price: 149.91 EUR
Availability: InStock

Applications in Quantum Theory

Autor: John S. Avery

Jazyk:

Väzba: Brožovaná

Vydavateľ: Springer Netherlands

Dostupnosť: Skladom u dodávateľa

Odosielame za 5-8 dní

149.91 €

where d 3 3)2 ( L x - -- i3x j3x j i ij Thus the Gegenbauer polynomials play a role in the theory of...

Informácie o knihe

Autor

John S. Avery

Jazyk

Angličtina

Väzba

Kniha - Brožovaná

Vydalo

2012

Stránok

256

EAN

9789401075442

ISBN

9401075441

Enbook ID

02177902

Vydavateľ

Springer Netherlands

Hmotnosť

427

Rozmery

156 x 236 x 14

Kompletný popis

where d 3 3)2 ( L x - -- i3x j3x j i ij Thus the Gegenbauer polynomials play a role in the theory of hyper spherical harmonics which is analogous to the role played by Legendre polynomials in the familiar theory of 3-dimensional spherical harmonics; and when d = 3, the Gegenbauer polynomials reduce to Legendre polynomials. The familiar sum rule, in 'lrlhich a sum of spherical harmonics is expressed as a Legendre polynomial, also has a d-dimensional generalization, in which a sum of hyper spherical harmonics is expressed as a Gegenbauer polynomial (equation (3-27": The hyper spherical harmonics which appear in this sum rule are eigenfunctions of the generalized angular monentum 2 operator A , chosen in such a way as to fulfil the orthonormality relation: VIe are all familiar with the fact that a plane wave can be expanded in terms of spherical Bessel functions and either Legendre polynomials or spherical harmonics in a 3-dimensional space. Similarly, one finds that a d-dimensional plane wave can be expanded in terms of HYPERSPHERICAL HARMONICS xii "hyperspherical Bessel functions" and either Gegenbauer polynomials or else hyperspherical harmonics (equations ( 4 - 27) and ( 4 - 30) ) : 00 ik·x e = (d-4)!!A~oiA(d+2A-2)j~(kr)C~(~k'~) 00 (d-2)!!I(0) 2: iAj~(kr) 2:Y~ (["2k)Y (["2) A A=O ). l). l)J where I(O) is the total solid angle. This expansion of a d-dimensional plane wave is useful when we wish to calculate Fourier transforms in a d-dimensional space.

Mohlo by vás zaujímať

Zákazníci, ktorí si kúpili túto knihu, kúpili tiež

Najčastejšie vyhľadávané

Categories

Authors

Publishers

Produkty

Produkty

Najčastejšie vyhľadávané

Categories

Authors

Publishers

Produkty

Produkty

Hyperspherical Harmonics

Applications in Quantum Theory

Informácie o knihe

Kompletný popis

Mohlo by vás zaujímať

Zákazníci, ktorí si kúpili túto knihu, kúpili tiež