The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential
✍ Scribed by D. I. Borisov; R. R. Gadyl’shin
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2006
- Tongue
- English
- Weight
- 111 KB
- Volume
- 147
- Category
- Article
- ISSN
- 0040-5779
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## Abstract We show that when a potential __b~n~__ of a discrete Schrödinger operator, defined on __l__^2^(ℤ^+^), slowly oscillates satisfying the conditions __b~n~__ ∈ __l__^∞^ and ∂__b~n~__ = __b__~__n__ +1~ – __b~n~__ ∈ __l^p^__, __p__ < 2, then all solutions of the equation __Ju__ = __Eu__ are
We study the spectrum of Schrödinger operators with a uniform potential on the lth shell of the d-regular tree. As a result, we show the relationship between the spectral structure and the intensities of the potential. Furthermore we completely determine the discrete eigenvalues with their multiplic