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Planar Quantum Mechanics: an Intriguing Supersymmetric Example

After setting up a Hamiltonian formulation of planar (matrix) quantum mechanics, we illustrate its effectiveness in a non-trivial supersymmetric example. The numerical and analytical study of two sectors of the model, as a function of 't Hooft's coupling $λ$, reveals both a phase transition at $λ=1$ (disappearence of the mass gap and discontinuous jump in Witten's index) and a new form of strong-weak duality for $λ\to 1/λ$.