Two phases of the noncommutative quantum mechanics

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We consider quantum mechanics on the noncommutative plane in the presence of magnetic field B. We show, that the model has two essentially different phases separated by the point Bθ=cℏ²/e, where θ is a parameter of noncommutativity. In this point the system reduces to exactly-solvable one-dimensional system. When κ=1-eBθ/cℏ²<0 there is a finite number of states corresponding to the given value of the angular momentum. In another phase, i.e. when κ>0 the number of states is infinite. The perturbative spectrum near the critical point κ=0 is computed.