Journal of Statistical Physics, Vol. 75. Nos. 1/2. 1994. p. 317-335.
The discrete analog of the tight binding approximation is investigated. Let lambda_0 be some energy level of a real discrete potential q. Then there exists an energy band for a one-dimensional 2N-periodic chain of the same atoms which lies near lambda_0. We study the asymptotic behavior of this band when N tends to infinity.