• SUSYQM and other symmetries in...

Result: SUSYQM and other symmetries in quantum mechanics

Title:
SUSYQM and other symmetries in quantum mechanics
Authors:
LEVAI, G
Source:
International Conference on Progress in Supersymmetric Quantum Mechanics (PSQM'03) (Valladolid, Spain, 15-19 July 2003)Journal of physics. A, mathematical and general. 37(43):10179-10191
Publisher Information:
Bristol: Institute of Physics, 2004.
Publication Year:
2004
Physical Description:
print, 40 ref
Original Material:
INIST-CNRS
Subject Terms:
Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Generalites, General, Physiques classique et quantique: mécanique et champs, Classical and quantum physics: mechanics and fields, Mécanique quantique, Quantum mechanics, Méthodes algébriques, Algebraic methods, Physique des particules elementaires et champs, The physics of elementary particles and fields, Théorie générale des champs et particules, General theory of fields and particles, Symétries et lois de conservation, Symmetry and conservation laws, Supersymétrie, Supersymmetry, Equation différentielle linéaire, Linear differential equations, Factorisation, Factorization, Groupe SU(1,1), SU(1,1) group, Grupo SU(1,1), Mécanique quantique supersymétrique, Supersymmetric quantum mechanics, Opérateur, Operator, Operador, Ordre 1, First order, Orden 1, Théorie SU(2), SU(2) theory, Superpotentiel, Superpotential, Superpotencial
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Institute of Nuclear Research of the Hungarian Academy of Sciences, PO Box 51, 4001 Debrecen, Hungary
ISSN:
0305-4470
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=16222659
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Physics of elementary particles and fields

Theoretical physics
Accession Number:
edscal.16222659
Database:
PASCAL Archive

Further Information

The relation of supersymmetric quantum mechanics (SUSYQM) is discussed with two other symmetry-based approaches: PT symmetry and a differential realization of the su(1, 1) and su(2) algebra. It is demonstrated that PT 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 PT 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 At 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.