Perturbations of Supersymmetric Systems in Quantum Mechanics

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


The methods of supersymmetry are extended to the factorization method. The degeneracy of levels in factorizable systems is broken under perturbations. With the methods of supersymmetry it is possible to state laws on the order of these perturbed energy levels. One proof of a confirmation of these laws has a more algebraic touch and works for first order perturbation theory. The proof of the laws beyond perturbation theory is hard, more of an analytic spirit and exploits convexity properties of the potentials. The convexity properties serve also for an intuitive argument. An important application is the law on the ordering of energy levels in atoms.


Harmonic Oscillator Factorizable System Level Spacing Ground State Wave Function Order Perturbation Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    E. Schrödinger, A method of determining quantum-mechanical eigenvalues and eigen-functions, Proc. Roy. Irish Acad. A46, (1940) 9–16.zbMATHGoogle Scholar
  2. [2]
    E. Schrödinger, Further studies on solving eigenvalue problems by factorization, Proc. Roy. Irish Acad. A46, (1941) 183.zbMATHGoogle Scholar
  3. [3]
    L. Infeld, T.E. Hull, The factorization medhod, Rev. Mod. Phys. 23, (1951), 21–68.MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. [4]
    E. Witten, Dynamical breaking of supersymmetry, Nucl. Phys. B188, (1981), 513–554.ADSzbMATHCrossRefGoogle Scholar
  5. [5]
    A.K. Ramdas, S. Rodriguez, Spectroscopy of the solid-state anologues of the hydrogen atom: donors and acceptors in semiconductors, Rep. Progr. Phys. 44, (1981), 1297.ADSCrossRefGoogle Scholar
  6. [6]
    B. Baumgartner, A. Pflug, A new approach to the understanding of level ordering in atoms and nuclei, preprint UWThPh-1989–11 to appear in Amer. J. Phys.Google Scholar
  7. [7]
    P.A. Deift, Applications of a commutation formula, Duke Math. J. 45, (1978), 267.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    B. Baumgartner, Level Comparison Theorems, Ann. Phys. 168, (1986), 484–526.MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • B. Baumgartner
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienViennaAustria

Personalised recommendations