Abstract
The relation of supersymmetric quantum mechanics (SUSYQM) is discussed with two other symmetry-based approaches: symmetry and a differential realization of the su(1, 1) and su(2) algebra. It is demonstrated that symmetry imposes conditions on the even and odd parts of the real and imaginary components of the superpotential W(x), and these are expressed in terms of a system of first-order linear differential equations, which is homogeneous when the factorization energy is real and inhomogeneous when it is complex. The formal solution of this system is presented for various special cases as well as for the general case. It is shown that a trivial solution of this system corresponds to the unbroken symmetry for the Scarf II potential. The formalism of SUSYQM is also linked with that of the potential algebra approach, and it is demonstrated that the J+ and J? ladder operators of some su(1, 1) or su(2) algebras act on series of degenerate levels of different potentials essentially in the same way as the A and A? shift operators of SUSYQM. Examples are presented for su(1, 1) and su(2) potential algebras, as well as for spectrum generating algebras of the same type. Possible generalizations of this construction are also pointed out.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
