Inverse spectral problem for the Schrödinger equation with periodic vector potential (Q910979)

The author considers the Schrödinger equation \[ H\Psi =\lambda \Psi \quad or\quad (i(\partial /\partial x_ 1)+A_ 1(x))^ 2\Psi +(i(\partial /\partial x_ 2)+A_ 2(x))^ 2\Psi +V(x)\Psi (x)=\lambda \Psi (x), \] with \(\bar A(x)=(A_ 1(x),A_ 2(x))\) is the vector potential, and V(x) is the scalar potential. \(H_ 0\) is the periodic spectrum of H, \(H_ r\) is the Floquet spectrum of H, and B is the curl of \(\bar A.\) He studies the inverse spectrum problem of recovering B(x) and V(x) from \(H_ 0\) or \(H_ r\).