INTERTWINING OF EXACTLY SOLVABLE DIRAC EQUATIONS WITH ONE-DIMENSIONAL POTENTIALS

被引:32
作者
ANDERSON, A [1 ]
机构
[1] UNIV UTAH, DEPT PHYS, SALT LAKE CITY, UT 84112 USA
关键词
D O I
10.1103/PhysRevA.43.4602
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
The method of intertwining is used to construct transformations between one-dimensional electric potentials or one-dimensional external scalar fields for which the Dirac equation is exactly solvable. The transformations are analogous to the Darboux transformations between Schrodinger potentials. It is shown that a class of exactly solvable Dirac potentials corresponds to soliton solutions of the modified Korteweg-deVries (MKdV) equation, just as certain Schrodinger potentials are solitons of the Korteweg-deVries equation. It is also shown that the intertwining transformations are related to Backlund transformations for MKdV. The structure of the intertwining relations is shown to be described by an N = 4 superalgebra, generalizing supersymmetric quantum mechanics to the Dirac case.
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收藏
页码:4602 / 4610
页数:9
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