Spectrum-Generating Superalgebra for Linear Harmonic Oscillators
classification
🧮 math-ph
hep-thmath.MP
keywords
harmoniclinearspectrum-generatingsuperalgebraoscillatoralgebraicappearanceappropriate
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We show that the Hilbert space of the standard linear harmonic oscillator is a complete orbit of the osp(2,1;2) spectrum-generating superalgebra, and that this is the smallest such algebraic structure. The ubiquitous appearance of the linear harmonic oscillator in virtually all domains of theoretical physics guarantees a corresponding ubiquity of appropriate generalizations of this spectrum-generating superalgebra.
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