✦ LIBER ✦
Möbius inversion on a multiplicative semigroup and inverse lattice problems in physics
✍ Scribed by Chen Zhaodou; Shen Yanan; Liu Shaojun
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 102 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
✦ Synopsis
The generalized Mo¨bius function and Mo¨bius inversion formula are applied to a multiplicative semigroup. A general mathematical method based on this Mo¨bius inversion is presented to solve inversion problems of expansions with unequally weighted terms. By this method, all the inverse lattice problems in physics can be solved concisely. The solutions of four inverse lattice problems: the Fibonacci structure, the square lattice structure, the bcc and the hcp lattice structures are given. These are difficult to be solved by other methods.