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Paper   IPM / Physic / 7207
School of Physics
  Title:   Two Dimensional Hamiltonian with Generalized Shape Invariance Symmetry
  Author(s): 
1.  H. Panahi-Talemi
2.  M.A. Jafarizadeh
  Status:   In Proceedings
  Proceeding: Proceedings of the Third International Conference on Geometry, Integrability and Quantization, Varna, Bulgaria, June 14-23, 2001
  No.:  0
  Year:  2001
  Supported by:  IPM
  Abstract:
The two dimensional Hamiltonian with generalized shape invariance symmetry over S2, has been obtained via Fourier transformation over the three coordinates of the SU(3) Casimir operator defined on SU(3)/SU(2) symmetric space. It is shown that the generalized shape invariance is equivalent to SU(3) symmetry and that there is one to one correspondence between the representations of the generalized shape invariance and SU(3) Verma modules. Also the two dimensional Hamiltonian in R2 space which posseses ordinary shape invariance symmetry with respect to two parameters, has been obtained via In?n?Wigner contraction over SU(3) manifold.

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