Shape Invariant Potential and Semi-Unitary Transformations (SUT) for Supersymmetric Harmonic Oscillator in T4-Space
P. S. Bisht, O. P. S. Negi
TL;DR
This paper develops semi-unitary transformations to generate supersymmetric partner Hamiltonians for a harmonic oscillator in T4-space, revealing ground state loss and basis completeness in a modified Hilbert space.
Contribution
It introduces a novel semi-unitary transformation framework for supersymmetric quantum mechanics in T4-space, highlighting unique spectral properties.
Findings
The supersymmetric partner loses its ground state in T4-space.
Eigenfunctions form a complete orthonormal basis in a subspace.
Transformation affects the spectral structure of the harmonic oscillator.
Abstract
Constructing the Semi - Unitary Transformation (SUT) to obtain the supersymmetric partner Hamiltonians for a one dimensional harmonic oscillator, it has been shown that under this transformation the supersymmetric partner loses its ground state in T^{4}- space while its eigen functions constitute a complete orthonormal basis in a subspace of full Hilbert space. Keywords: Supersymmetry, Superluminal Transformations, Semi Unitary Transformations. PACS No: 14.80Lv
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