Supersymmetric Quantum Mechanics
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.
KeywordsDirac Operator Susy Model Ground State Wave Function Factorization Scheme SUPERSYMMETRIC Quantum Mechanics
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- L.E. Gendenshtein and I.V. Krive, Usp. Fiz. Nauk 146 (1986) 645.Google Scholar
- A. Stahlhofen and K. Bleuler, “An Algebraic Form of the Factorization Method”, Duke Univ./Univ. of Bonn preprint (1988).Google Scholar
- L. Infeld and T.E. Hull, Rev. Mod. Phys. 23 (1951) 21.Google Scholar
- K. Chadan and P.C. Sabatier, “Inverse Problems in Quantum Scattering Theory”, Springer 1989.Google Scholar
- 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
- H. Grosse and L. Pittner, Jour. of Phys. A: Math. Gen.Google Scholar
- D. Bollé, P. Dupont and II. Grosse, “On the General Structure of Quantum Mechanical Susy Models”, Univ. Leuwen preprint 1989.Google Scholar