# Harmonic oscillator chains as Wigner quantum systems: Periodic and fixed wall boundary conditions in gl(1|n) solutions

@article{Lievens2007HarmonicOC, title={Harmonic oscillator chains as Wigner quantum systems: Periodic and fixed wall boundary conditions in gl(1|n) solutions}, author={Stijn Lievens and N I Stoilova and Joris Van der Jeugt}, journal={Journal of Mathematical Physics}, year={2007}, volume={49}, pages={073502} }

We describe a quantum system consisting of a one-dimensional linear chain of n identical harmonic oscillators coupled by a nearest neighbor interaction. Two boundary conditions are taken into account: periodic boundary conditions (where the nth oscillator is coupled back to the first oscillator) and fixed wall boundary conditions (where the first oscillator and the nth oscillator are coupled to a fixed wall). The two systems are characterized by their Hamiltonian. For their quantization, we…

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