Supersymmetric Quantum Mechanics

  • H. Grosse
Part of the Mathematical Physics Studies book series (MPST, volume 12)


We summarize recent developments of supersymmetric quantum mechanics. We start from the susy oscillator, mention the factorization schemes and discuss the order of levels of Schrödinger operators as an example. We mention soliton equations and the inverse scattering problem and discuss susy breaking and index problems for Dirac operators. The construction of Lie-supergroups suggests a generalization of the well-known theorems of von Neumann and Wigner to superspace. We mention finally studies of the general structure of susy models. A number of relations between the operator formulation and the stochastic formulation result.


Dirac Operator Susy Model Ground State Wave Function Factorization Scheme SUPERSYMMETRIC Quantum Mechanics 
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  1. [1]
    J. Wess and B. Zumino, Nucl. Phys. B70 (1974) 39.MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    V.A. Kostelecky and D.K. Campbell, Physica 15D (1985) 1.MathSciNetADSGoogle Scholar
  3. [3]
    M.F. Sohnius, Phys. Rep. 128 (1985) 39.MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    E. Witten, Nucl. Phys. B185 (1981) 513.ADSCrossRefGoogle Scholar
  5. [5]
    P. Salomonson and J.W. van Holten, Nucl. Phys. B196 (1982) 509.ADSCrossRefGoogle Scholar
  6. [6]
    M. de Crombrugghe and V. Rittenberg, Ann. Phys. NY 151 (1983) 99.ADSCrossRefGoogle Scholar
  7. [7]
    L.E. Gendenshtein and I.V. Krive, Usp. Fiz. Nauk 146 (1986) 645.Google Scholar
  8. [8]
    P.A. Deift, Duke Math. Journal 45 (1978) 267.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    A. Stahlhofen and K. Bleuler, “An Algebraic Form of the Factorization Method”, Duke Univ./Univ. of Bonn preprint (1988).Google Scholar
  10. [10]
    L. Infeld and T.E. Hull, Rev. Mod. Phys. 23 (1951) 21.Google Scholar
  11. [11]
    C.V. Sukumar, J. Phys. A18 (1985) L 697.MathSciNetADSGoogle Scholar
  12. [12]
    A. Stahlhofen, J. Phys. A: Math. Gen. 22 (1989) 1053.MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    H. Grosse and A. Martin, Phys. Rep. 60 (1980) 341.MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    H. Grosse and A. Martin, Phys. Lett. 134B (1984) 368.MathSciNetADSGoogle Scholar
  15. [15]
    B. Baumgartner, H. Grosse and A. Martin, Phys. Lett. 146B (1984) 363.MathSciNetADSGoogle Scholar
  16. [16]
    H. Grosse, Phys. Lett. 197 (1987) 413.MathSciNetGoogle Scholar
  17. [17]
    K. Chadan and P.C. Sabatier, “Inverse Problems in Quantum Scattering Theory”, Springer 1989.Google Scholar
  18. [18]
    F. Gesztesy, H. Grosse and B. Thaller, Phys. Lett. 116B (1982) 155.ADSGoogle Scholar
  19. [19]
    D. Bollé, F. Gesztesy and B. Simon, Lett. Math. Phys. 13 (1987) 127; and same authors with W. Schweiger, Jour. Math. Phys. 28 (1987) 1512.Google Scholar
  20. [20]
    A. Jaffe, A. Lesniewski and M. Lewenstein, Ann. of Phys. NY 178 (1987) 313.MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. [21]
    A. Jaffe, A. Lesniewski and J. Weitsman, Commun. Math. Phys. 112 (1987) 75.MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. [22]
    H. Grosse and L. Pittner, Jour. of Phys. A: Math. Gen. 20 (1987) 4265 and 21 (1988) 3239.MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    H. Grosse and L. Pittner, Jour. Math. Phys. 29 (1988) 110.MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. [24]
    H. Grosse and L. Pittner, Jour. of Phys. A: Math. Gen.Google Scholar
  25. [25]
    D. Bollé, P. Dupont and II. Grosse, “On the General Structure of Quantum Mechanical Susy Models”, Univ. Leuwen preprint 1989.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • H. Grosse
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienViennaAustria

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