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We construct a nonrelativistic wave equation for spinning particles in thenoncommutative space (in a sense, a $\theta$-modification of the Pauliequation). To this end, we consider the nonrelativistic limit of the$\theta$-modified Dirac equation. To complete the consideration, we present apseudoclassical model (\`a la Berezin-Marinov) for the correspondingnonrelativistic particle in the noncommutative space. To justify the lattermodel, we demonstrate that its quantization leads to the $\theta$-modifiedPauli equation. We extract $\theta$-modified interaction between anonrelativistic spin and a magnetic field from such a Pauli equation andconstruct a $\theta$-modification of the Heisenberg model for two coupled spinsplaced in an external magnetic field. In the framework of such a model, wecalculate the probability transition between two orthogonal EPR(Einstein-Podolsky-Rosen) states for a pair of spins in an oscillatory magneticfield and show that some of such transitions, which are forbidden in thecommutative space, are possible due to the space noncommutativity. This allowsus to estimate an upper bound on the noncommutativity parameter.

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space