An exactly solvable periodic Schrodinger operator

The authors explicitly determine the band spectrum of a periodically strongly singular Schrodinger operator in L 2 (R) associated with the differential expression -d 2 /dx 2 +(s 2 -1/4)/cos 2 x+(s' 2 -1/4)/sin 2 x, x epsilon R,x epsilon pi Z/2, 0<s,s'<1. The corresponding density of states is calculated analytically.