ABSTRACT
After introducing Wigner Quantum Systems, we give a short review of the one-dimensional Wigner Quantum Oscillator. Then we define the threedimensional N-particle Wigner Quantum Oscillator, and its relation to the Lie superalgebra https://www.w3.org/1998/Math/MathML"> s l ( 1 ∣ 3 N ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq8956.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . In this framework (and first for https://www.w3.org/1998/Math/MathML"> N = 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq8957.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , energy, coordinates, momentum and the angular momentum of the particles are investigated.
