Spectral properties of adiabatically perturbed differential operators with periodic coefficients. (English) Zbl 0726.34068

Buslaev, V. S.

Recent developments in quantum mechanics, Proc. Conf., Braşov/Rom. 1989, Math. Phys. Stud. 12, 97-112 (1991).

Summary: [For the entire collection see Zbl 0722.00044.]
We describe the asymptotic structure of the spectrum and the asymptotic behavior of the eigenfunctions of the operators \[ Hz=- z_{xx}+p(x)z+v(\epsilon x)z, \] p is periodic \(0<\epsilon \ll 1\).

MSC:

34L20

Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators

Keywords:

asymptotic structure of the spectrum; asymptotic behavior of the eigenfunctions; periodic

Citations:

Zbl 0722.00044