2ND-ORDER DERIVATIVE SUPERSYMMETRY, Q-DEFORMATIONS AND THE SCATTERING PROBLEM

被引:163
作者
ANDRIANOV, AA
IOFFE, MV
CANNATA, F
DEDONDER, JP
机构
[1] DIPARTIMENTO FIS, I-40126 BOLOGNA, ITALY
[2] IST NAZL FIS NUCL, I-40126 BOLOGNA, ITALY
[3] UNIV PARIS 07, PHYS NUCL LAB, F-75251 PARIS 05, FRANCE
[4] INST PHYS NUCL LYON, DIV PHYS THEOR, F-91406 ORSAY, FRANCE
来源
INTERNATIONAL JOURNAL OF MODERN PHYSICS A | 1995年 / 10卷 / 18期
关键词
D O I
10.1142/S0217751X95001261
中图分类号
O57 [原子核物理学、高能物理学];
学科分类号
070202 ;
摘要
In a search for pairs of quantum systems linked by dynamical symmetries, we give a systematic analysis of novel extensions of standard one-dimensional supersymmetric quantum mechanics. The most general supercharges involving higher order derivatives are introduced, leading to an algebra which incorporates a higher order polynomial of the Hamiltonian. We investigate the condition for irreducibility of such a higher order generator to a product of standard first derivative Darboux transformations. As a new example of application of this approach we study the quantum-mechanical radial problem including the scattering amplitudes. We also investigate the links between this higher derivative SUSY and a q-deformed supersymmetric quantum mechanics and introduce the notion of self-similarity in momentum space. An explicit model for the scattering amplitude is constructed in terms of a hypergeometric function which corresponds to a reflectionless potential with infinitely many bound states.
引用
收藏
页码:2683 / 2702
页数:20
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