The Schrodinger Equation on Non-Stationary Domains
| dc.contributor.author | Karner, Gunther | |
| dc.date.accessioned | 2019-03-19T18:07:42Z | |
| dc.date.available | 2019-03-19T18:07:42Z | |
| dc.date.issued | 1998-07-17 | |
| dc.description.abstract | We investigate the dynamical effects of non-stationary boundaries on the stability of a quantum Hamiltonian system described by a periodic family {H(γ, t), t ∈ [0, Γ], Γ > 0} of Sturm-Liouville operators, a Schrödinger equation i∂tψ = H(γ, t)ψ defined on Ω(α) = {(t, x) ∈ ℝ2 : x ∈ (α(t), ∞), α ∈ C3(ℝ), α(t) = α(t + kΓ), k ∈ ℤ}, as well as boundary conditions at x = α(t) modeled by the Γ-periodic function γ. Employing extended Hilbert space methods, stability conditions for the spectra of the evolution operators U(α, γ, Γ, 0) to the families {H(γ, t)} under perturbations induced by variations of boundary oscillations, respectively conditions, are derived. In particular, it is shown that the existence of a pure point finitely degenerate realization U(a, γˆ, Γ, 0)) implies pure point U(a, γ, Γ, 0) for all γ ∈ C1(ℝ), α ∈ C3(ℝ), whereas in case of infinitely degenerate σpp (U(α, γˆ, Γ, 0)) the existence of σac (U(α, γ, Γ, 0)) ≠ 0, respectively σsc(U (a, γ, Γ, 0)) ≠ ∅, is possible. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Karner, G. (1998). The Schrodinger equation on non-stationary domains. <i>Electronic Journal of Differential Equations, 1998</i>(20), pp. 1-20. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/7934 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 1998, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Stability of dense point spectra | |
| dc.subject | Boundary induced perturbations | |
| dc.subject | Krein's resolvent formula | |
| dc.title | The Schrodinger Equation on Non-Stationary Domains | |
| dc.type | Article |