This article provides a fully consistent group theoretical procedure for finding atomic hybrids on a sphere and for relating them to the matrices representing the operators x, y, and z with respect to given basis functions. The tetrahedral, octahedral, and cubic hybrids based on the cube are derived
On a property of functions on the sphere and its application
β Scribed by Yuhong Liu
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 247 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
We prove that a class of invariant functions, admissible with respect to the Fubini-Study metric on the sphere S 2 = P 1 C are bounded from below by a function going to infinity on the intersection of charts. This lower bound is sharp in terms of an HΕrmander type inequality.
A function which is homogeneous in x y z of degree n and satisfies V xx + V yy + V zz = 0 is called a spherical harmonic. In polar coordinates, the spherical harmonics take the form r n f n , where f n is a spherical surface harmonic of degree n. On a sphere, f n satisfies f n + n n + 1 f n = 0, whe