Inverse Square Potential in a Space with Spin Noncommutativity of Coordinates
Keywords:inverse square potential, noncommutativity
An attractive inverse square potential has been considered in a space with the spin noncommutativity of coordinates. The corresponding effective potential energy, as well as the total energy, is shown to be bounded from below. Using the variational method, the upper limit of the ground-state energy, which turns out to be negative for a sufficiently large coupling constant, is found. As a result, it is proved that the inverse square potential creates stationary levels in the space concerned, unlike the case of commutative space, where a particle falls to the center.
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