Geodesic
On spectral properties of one-dimensional disperse crystals
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VI, Tome 133 (1984), pp. 197-211

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The connection between spectral characteristics of one-dimensional Schrödinger operator $l_a(y)=-y''+q_a(x)y$ with a periodic potential $q_a=\sum_{n=-\infty}^\infty q(x-na)$ as $a\to\infty$ and spectral characteristics of the Schrödinger operator $l(y)=-y''+q(x)y$ with decreasing potential $q(x)$ is studed. 
@article{ZNSL_1984_133_a13,
     author = {B. S. Pavlov and N. V. Smirnov},
     title = {On spectral properties of one-dimensional disperse crystals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {197--211},
     publisher = {mathdoc},
     volume = {133},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_133_a13/}
}
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B. S. Pavlov; N. V. Smirnov. On spectral properties of one-dimensional disperse crystals. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VI, Tome 133 (1984), pp. 197-211. http://geodesic.mathdoc.fr/item/ZNSL_1984_133_a13/