 |
|
Resonances for Slowly Varying Perturbations of a Periodic Schrödinger Operator |
Canad. J. Math. 54(2002), 998-1037
Published:2002-10-01
Printed: Oct 2002
Printed: Oct 2002
- Mouez Dimassi
Abstract
We study the resonances of the operator $P(h) = -\Delta_x + V(x) +
\varphi(hx)$. Here $V$ is a periodic potential, $\varphi$ a
decreasing perturbation and $h$ a small positive constant. We prove
the existence of shape resonances near the edges of the spectral bands
of $P_0 = -\Delta_x + V(x)$, and we give its asymptotic expansions in
powers of $h^{\frac12}$.
| MSC Classifications: |
35P99 - None of the above, but in this section 47A60 - Functional calculus 47A40 - Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx] |