Abstract
We show that there exist a large class of new nontrivial exactly solvable models with their potentials depending only on one spatial variable on a 2D noncommutative plane and show that their general solutions are Schr\"odinger cat states. This feature not only establishes an interesting connection between quantum mechanics on noncommutative spaces and quantum information science but also shed light on proposing new schemes based on the quantum entanglement to test the noncommutativity.
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