Coupling constant thresholds of perturbed periodic Hamiltonians
| dc.contributor | Virginia Tech | en |
| dc.contributor.author | Fassari, S. | en |
| dc.contributor.author | Klaus, Martin | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessed | 2014-03-20 | en |
| dc.date.accessioned | 2014-04-09T18:12:17Z | en |
| dc.date.available | 2014-04-09T18:12:17Z | en |
| dc.date.issued | 1998-09 | en |
| dc.description.abstract | We consider Schrodinger operators of the form H-lambda= -Delta + V + lambda W on L-2(R-v) (v=1, 2, or 3) with V periodic, W short range, and lambda a real non-negative parameter. Then the continuous spectrum of H-lambda has the typical band structure consisting of intervals, separated by gaps. In the gaps there may be discrete eigenvalues of H-lambda that are functions of the parameter lambda. Let (a,b) be a gap and E(lambda)E(a,b) an eigenvalue of H-lambda. We study the asymptotic behavior of E(lambda) as lambda approaches a critical value lambda(0), called a coupling constant threshold, at which the eigenvalue either emerges from or is absorbed into the continuous spectrum. A typical question is the following: Assuming E(lambda)down arrow a as lambda down arrow lambda(0), is E(lambda)-a similar to c(lambda - lambda(0))(alpha) for some alpha>0 and c not equal 0, or is there an expansion in some other quantity? As one expects from previous work in the case V=0, the answer strongly depends on v. (C) 1998 American Institute of Physics. | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Fassari, S.; Klaus, M., "Coupling constant thresholds of perturbed periodic Hamiltonians," J. Math. Phys. 39, 4369 (1998); http://dx.doi.org/10.1063/1.532516 | en |
| dc.identifier.doi | https://doi.org/10.1063/1.532516 | en |
| dc.identifier.issn | 0022-2488 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/47036 | en |
| dc.identifier.url | http://scitation.aip.org/content/aip/journal/jmp/39/9/10.1063/1.532516 | en |
| dc.language.iso | en | en |
| dc.publisher | AIP Publishing | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | h-lambda-w | en |
| dc.subject | schrodinger-operators | en |
| dc.subject | eigenvalues | en |
| dc.subject | sigma(h) | en |
| dc.subject | behavior | en |
| dc.subject | gap | en |
| dc.title | Coupling constant thresholds of perturbed periodic Hamiltonians | en |
| dc.title.serial | Journal of Mathematical Physics | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |
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