Geodesic
Some spectral identities for the one-dimensional hill operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 37 (1978) no. 2, pp. 281-288 
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/
@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},
     year = {1978},
     volume = {37},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_37_2_a12/}
}
TY  - JOUR
AU  - N. E. Firsova
TI  - Some spectral identities for the one-dimensional hill operator
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1978
SP  - 281
EP  - 288
VL  - 37
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1978_37_2_a12/
LA  - ru
ID  - TMF_1978_37_2_a12
ER  - 
%0 Journal Article
%A N. E. Firsova
%T Some spectral identities for the one-dimensional hill operator
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1978
%P 281-288
%V 37
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1978_37_2_a12/
%G ru
%F TMF_1978_37_2_a12

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] E. Ch. Titchmarsh, Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, t. 2, IL, 1961, str. 555 | MR

[2] Dzh. Zaiman, Printsipy teorii tverdogo tela, «Mir», 1974

[3] N. E. Firsova, Matematicheskie voprosy teorii rasprostraneniya voln, no. 7, LGU, 1975, 183 | MR

[4] N. E. Firsova, Matem. zametki, 18 (1975), 831 | MR | Zbl