SUSY-hierarchy of one-dimensional reflectionless potentials
Description
A class of one-dimensional reflectionless potentials, an absolute transparency of which is concerned with their belonging to one SUSY-hierarchy with a constant potential, is studied. An approach for determination of a general form of the reflectionless potential on the basis of construction of such a hierarchy by the recurrent method is proposed. A general form of interdependence between superpotentials with neighboring numbers of this hierarchy, opening a possibility to find new reflectionless...[Show more]
dc.contributor.author | Maydanyuk, Sergei | |
---|---|---|
dc.date.accessioned | 2004-10-19 | |
dc.date.accessioned | 2005-03-10 | |
dc.date.accessioned | 2011-01-05T08:56:05Z | |
dc.date.available | 2005-03-10 | |
dc.date.available | 2011-01-05T08:56:05Z | |
dc.date.created | 2004 | |
dc.identifier.uri | http://hdl.handle.net/1885/42656 | |
dc.identifier.uri | http://digitalcollections.anu.edu.au/handle/1885/42656 | |
dc.description.abstract | A class of one-dimensional reflectionless potentials, an absolute transparency of which is concerned with their belonging to one SUSY-hierarchy with a constant potential, is studied. An approach for determination of a general form of the reflectionless potential on the basis of construction of such a hierarchy by the recurrent method is proposed. A general form of interdependence between superpotentials with neighboring numbers of this hierarchy, opening a possibility to find new reflectionless potentials, have a simple analytical view and are expressed through finite number of elementary functions (unlike some reflectionless potentials, which are constructed on the basis of soliton solutions or are shape invariant in one or many steps with involving scaling of parameters, and are expressed through series), is obtained. An analysis of absolute transparency existence for the potential which has the inverse power dependence on space coordinate (and here tunneling is possible) is fulfilled. A SUSY-hierarchy of the inverse power reflectionless potentials is constructed. Isospectral expansions of this hierarchy is analyzed. | |
dc.format.extent | 388540 bytes | |
dc.format.extent | 352 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | application/octet-stream | |
dc.language.iso | en_AU | |
dc.subject | exactly solvable model | |
dc.subject | reflectionless potentials | |
dc.subject | supersymmetric quantum mechanics | |
dc.subject | inverse power potentials | |
dc.subject | isospectral potentials | |
dc.title | SUSY-hierarchy of one-dimensional reflectionless potentials | |
dc.type | Working/Technical Paper | |
local.description.notes | In this paper I present the analysis of reflectionless peculiarities of quantum systems and some new results in this topic of physics. | |
local.description.refereed | yes | |
local.identifier.citationmonth | jul | |
local.identifier.citationyear | 2004 | |
local.identifier.eprintid | 2816 | |
local.rights.ispublished | inpress | |
dc.date.issued | 2004 | |
local.contributor.affiliation | Institute for Nuclear Research, National Academy of Science of Ukraine | |
local.contributor.affiliation | Laboratory of time analysis of nuclear processes | |
Collections | ANU Research Publications |
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