Geodesic
Perturbation theory formulas for the Schr\"odinger equation with a~nonsmooth periodic potential
Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 101-123

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Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schrödinger operator in $R^3$. An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation. 
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     author = {Yu. E. Karpeshina},
     title = {Perturbation theory formulas for the {Schr\"odinger} equation with a~nonsmooth periodic potential},
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Yu. E. Karpeshina. Perturbation theory formulas for the Schr\"odinger equation with a~nonsmooth periodic potential. Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 101-123. http://geodesic.mathdoc.fr/item/SM_1992_71_1_a7/