How Long to Read Hyperspherical Harmonics

How Long Does it Take to Read Hyperspherical Harmonics?

It takes the average reader 4 hours and 22 minutes to read Hyperspherical Harmonics by John S. Avery

Assuming a reading speed of 250 words per minute. Learn more

Description

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.

How long is Hyperspherical Harmonics?

Hyperspherical Harmonics by John S. Avery is 256 pages long, and a total of 65,536 words.

This makes it 86% the length of the average book. It also has 80% more words than the average book.

How Long Does it Take to Read Hyperspherical Harmonics Aloud?

The average oral reading speed is 183 words per minute. This means it takes 5 hours and 58 minutes to read Hyperspherical Harmonics aloud.

What Reading Level is Hyperspherical Harmonics?

Hyperspherical Harmonics is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Hyperspherical Harmonics?

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