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Hyperspherical Harmonics - Applications in Quantum Theory (Hardcover, 1989 ed.) Loot Price: R4,385
Discovery Miles 43 850
Hyperspherical Harmonics - Applications in Quantum Theory (Hardcover, 1989 ed.): John S. Avery

Hyperspherical Harmonics - Applications in Quantum Theory (Hardcover, 1989 ed.)

John S. Avery

Series: Reidel Texts in the Mathematical Sciences, 5

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Loot Price R4,385 Discovery Miles 43 850 | Repayment Terms: R411 pm x 12*

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where d 3 3)2 ( L x - -- i3x j3x j i i>j 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.

General

Imprint: Springer
Country of origin: Netherlands
Series: Reidel Texts in the Mathematical Sciences, 5
Release date: April 1989
First published: April 1989
Authors: John S. Avery
Dimensions: 235 x 155 x 17mm (L x W x T)
Format: Hardcover
Pages: 256
Edition: 1989 ed.
ISBN-13: 978-0-7923-0165-3
Categories: Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics) > General
LSN: 0-7923-0165-X
Barcode: 9780792301653

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