TY - JOUR

T1 - Effective masses and conformal mappings

AU - Kargaev, P.

AU - Korotyaev, E.

PY - 1995/5

Y1 - 1995/5

N2 - Let Gn, N∞N, denote the set of gaps of the Hill operator. We solve the following problems: 1) find the effective masses Mn±, 2) compare the effective mass Mn± with the length of the gap Gn, and with the height of the corresponding slit on the quasimomentum plane (both with fixed number n and their sums), 3) consider the problems 1), 2) for more general cases (the Dirac operator with periodic coefficients, the Schrödinger operator with a limit periodic potential). To obtain 1)-3) we use a conformal mapping corresponding to the quasimomentum of the Hill operator or the Dirac operator.

AB - Let Gn, N∞N, denote the set of gaps of the Hill operator. We solve the following problems: 1) find the effective masses Mn±, 2) compare the effective mass Mn± with the length of the gap Gn, and with the height of the corresponding slit on the quasimomentum plane (both with fixed number n and their sums), 3) consider the problems 1), 2) for more general cases (the Dirac operator with periodic coefficients, the Schrödinger operator with a limit periodic potential). To obtain 1)-3) we use a conformal mapping corresponding to the quasimomentum of the Hill operator or the Dirac operator.

UR - http://www.scopus.com/inward/record.url?scp=0002254974&partnerID=8YFLogxK

U2 - 10.1007/BF02099314

DO - 10.1007/BF02099314

M3 - Article

AN - SCOPUS:0002254974

VL - 169

SP - 597

EP - 625

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -