Geodesic
A~spectral identity for the multidimensional Schr\"odinger equation with periodic potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 524-528

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The Schrödinger equation with periodic potential is considered in the two- and three-dimensional cases. It is established that the sum of the determinants of the effective masses of the particle is equal to its real mass to the power equal to the dimension. 
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     author = {S. V. Frolov},
     title = {A~spectral identity for the multidimensional {Schr\"odinger} equation with periodic potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {524--528},
     publisher = {mathdoc},
     volume = {91},
     number = {3},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a15/}
}
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S. V. Frolov. A~spectral identity for the multidimensional Schr\"odinger equation with periodic potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 524-528. http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a15/