Geodesic
Electron zitterbewegung in a linear crystal with alternating parity
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 343-352 
S. V. Vonsovskii; M. S. Svirskii; L. M. Svirskaya. Electron zitterbewegung in a linear crystal with alternating parity. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 343-352. http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a11/
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     author = {S. V. Vonsovskii and M. S. Svirskii and L. M. Svirskaya},
     title = {Electron zitterbewegung in a~linear crystal with alternating parity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {343--352},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown thatin a linear periodic chain at whose sites electron wave functions of opposite parities alternate the existence of zitterbewegung of a nonrelativistic electron can be established without passage to the limiting case of a continuum. An analogy is established with the relations obtained earlier by the authors for the motion of a nonrelativistic electron in a two-site system. The zitterbewegung of the nonrelativistic electron in the considered system is given an interpretation analogous to the interpretation obtained by the first two authors for the zitterbewegung of a relativistic electron in Dirac's theory. A connection between the energy and effective mass of the nonrelativistic electron in the considered system is established.

[1] Vonsovskii S. V., Svirskii M. S., Svirskaya L. M., TMF, 85:2 (1990), 211–221

[2] Vonsovskii S. V., ZhTEF, 9 (1939), 154

[3] Cannota F., Ferrari L., Russo G., Solid State Commun., 74:4 (1990), 309 | DOI

[4] Vonsovskii S. V., Svirskii M. S, Problemy teoreticheskoi fiziki. Pamyati akad. I. E. Tamma, Nauka, M., 1972 | MR

[5] Cannota F., Ferrari L., Effects non relativistic zitterbewegung on the electron-phonon interaction in two-band system, Bologna, Italy, 1991

[6] Dirak P. A. M., Printsipy kvantovoi mekhaniki, Gl. XI. Relyativistskaya teoriya elektrona, Fizmatgiz, M., 1960 | MR

[7] Vonsovskii S. V., Svirskii M. S., Svirskaya L. M., FMM, 67 (1989), 985

[8] Ferrari L., Russo G., Phys. Rev.(B), 42:12 (1990), 7454 | DOI