Geodesic
Some spectral identities for the one-dimensional hill operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 37 (1978) no. 2, pp. 281-288

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Some relations are obtained between the Bloch functions (Floquet solution), the dispersion $d\lambda/dk$, the effective masses, and the real mass of a particle. In particuiar, it is shown that the sum of the effective masses of a particle converges absolutely and is equal to its real mass. 
@article{TMF_1978_37_2_a12,
     author = {N. E. Firsova},
     title = {Some spectral identities for the one-dimensional hill operator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {281--288},
     publisher = {mathdoc},
     volume = {37},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_37_2_a12/}
}
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N. E. Firsova. Some spectral identities for the one-dimensional hill operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 37 (1978) no. 2, pp. 281-288. http://geodesic.mathdoc.fr/item/TMF_1978_37_2_a12/