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Title: Coupled supersymmetric quantum mechanics: unifying the harmonic oscillator and supersymmetric quantum mechanics
Speaker: Cameron Williams (University of Houston)
Time: Friday, February 24, 2017 at 1:30 pm
Place: MONT 226Abstract: In this talk, we will briefly cover the standard quantum mechanical harmonic oscillator and the usual ladder operator technique for solving it. The ladder operator technique will be used to motivate traditional supersymmetric quantum mechanics. Supersymmetric quantum mechanics is useful for finding excited state energies of quantum systems, but has inherent flaws. Exact solutions via supersymmetric techniques are hard to come by and the (super)algebra of supersymmtric quantum mechanics is not very rich. Supersymmetric quantum mechanics is meant to mimic the quantum mechanical harmonic oscillator, however in general no true ladder structure exists. Returning to a treatment of the quantum mechanical harmonic oscillator under the guise of supersymmetry leads to a natural new structure which has flavors of both supersymmetry and the usual ladder structure from the harmonic oscillator. We call this new structure coupled supersymmetric quantum mechanics (coupled SUSY for short). Some results regarding the (Lie) algebraic structure underlying coupled SUSY, uncertainty principles, and coherent states for coupled SUSY will be discussed.