Stability and instability in quantum mechanics. (English) Zbl 0581.35078

Bellissard, J.

Schrödinger operators, Lect. 2nd 1984 Sess. C.I.M.E., Como/Italy, Lect. Notes Math. 1159, 204-229 (1985).

[For the entire collection see Zbl 0565.00010.]
The paper is the review of some results concerning the following topics: small divisors in quantum mechanics; time dependent Hamiltonians \(H_ 0+V(t)\) with the potentials periodic in time; the kicked rotator model, i.e. the model described as Hamiltonian formally given by \[ -\alpha \partial^ 2/\partial x^ 2+v(x)\sum^{\infty}_{n=-\infty}\delta (t- 2\pi n). \]

Reviewer: M.A.Perelmuter

MSC:

35Q99	Partial differential equations of mathematical physics and other areas of application
35J10	Schrödinger operator, Schrödinger equation
35B35	Stability in context of PDEs

Keywords:

review; small divisors; quantum mechanics; time dependent Hamiltonians; kicked rotator model

Citations:

Zbl 0565.00010