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The band-structure of a one-dimensional, periodic system in a scaling limit

โœ Scribed by Evans M Harrell

Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
989 KB
Volume
119
Category
Article
ISSN
0003-4916

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โœฆ Synopsis

The band-structure of one-dimensional Schrodinger operators is calculated when there are (a) high potential barriers (or deep wells), or (b) a wide lattice-spacing (i.e., the distance between minima of the potential). Explicit power-series formulae and error estimates are rigorously proved. The procedure used, a rigorous semi-classical method, is actually convergent for nonzero scaling parameters. Some general facts about the spectra are also discussed.

๐Ÿ“œ SIMILAR VOLUMES

The band-structure of a one-dimensional,
The band-structure of a one-dimensional, periodic system in a scaling limit: Evans M. Harrell. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
๐Ÿ“‚ Article ๐Ÿ“… 1979 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 66 KB

for which the action is finite and stationary under variations, without assuming any additional boundary conditions at infinity. An element of the proof is the vanishing of the stress tensor for a finite action solution, which actually holds true for the general O(N) o-model. For the two-dimensional