On the eigenvalues of Hill's equation
β Scribed by L. E. Blumenson
- Publisher
- John Wiley and Sons
- Year
- 1963
- Tongue
- English
- Weight
- 253 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For the k x k-matrix-valued version of Hill's equation it is shown that the dimension of the matrix needed to compute the Floquet exponents can be reduced from 2k to k. Also the existence of periodic solutions is equivalent to the non-invertibility of certain k x k-matrices.
The distribution of the ground state eigenvalue Ξ» 0 (Q) of Hill's operator Q = -d 2 /dx 2 + q(x) on the circle of perimeter 1 is expressed in two different ways in case the potential q is standard white noise. Let WN be the associated white noise measure, and let CBM be the measure for circular Brow