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Constructing the Semi - Unitary Transformation (SUT) to obtain thesupersymmetric partner Hamiltonians for a one dimensional harmonic oscillator,it has been shown that under this transformation the supersymmetric partnerloses its ground state in T^{4}- space while its eigen functions constitute acomplete orthonormal basis in a subspace of full Hilbert space.  Keywords: Supersymmetry, Superluminal Transformations, Semi UnitaryTransformations.  PACS No: 14.80L

Shape Invariant Potential and Semi-Unitary Transformations (SUT) for Supersymmetry Harmonic Oscillator in T 4-Space