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arXiv:hep-th/0608041 · International Journal of Theoretical Physics

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

P. S. Bisht, O. P. S. Negi

Published Oct 22, 2008• 0 citations
arXivHTMLPDF
DOI
10.1007/s10773-008-9872-1

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The unitary operator that transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different timescale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.