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In this article we present the cut Fock space approach to the D=d+1=2,Supersymmetric Yang-Mills Quantum Mechanics (SYMQM). We start by brieflyintroducing the main features of the framework. We concentrate on thoseproperties of the method which make it a convenient set up not only fornumerical calculations but also for analytic computations. In the main part ofthe article a sample of results are discussed, namely, analytic and numericalanalysis of the D=2, SYMQM systems with SU(2) and SU(3) gauge symmetry.

Exact solutions to D=2 Supersymmetric Yang-Mills Quantum Mechanics with SU(3) gauge group