Geodesic
Asymptotic Series for the Spectrum of the Schr\"odinger Operator for Layers Coupled Through Small Windows
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 3, pp. 407-418

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The asymptotic series for eigenvalues and bands for the Laplacian of the Dirichlet problem for three-dimensional layers coupled through small windows is constructed. We use the method of matching the asymptotic expansions of the solutions of boundary-value problems. 
@article{TMF_2002_131_3_a3,
     author = {I. Yu. Popov},
     title = {Asymptotic {Series} for the {Spectrum} of the {Schr\"odinger} {Operator} for {Layers} {Coupled} {Through} {Small} {Windows}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {407--418},
     publisher = {mathdoc},
     volume = {131},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_3_a3/}
}
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I. Yu. Popov. Asymptotic Series for the Spectrum of the Schr\"odinger Operator for Layers Coupled Through Small Windows. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 3, pp. 407-418. http://geodesic.mathdoc.fr/item/TMF_2002_131_3_a3/