On the Landau system in noncommutative phase-space

• An exact map between commutative and NC algebras with an effective Planck's constant.
• Connection of this generalized mapping with Moyal star product.
• Physically relevant quantities (magnetic-length, level-degeneracy, spectrum) computed using alternative variables.
• Demonstration of equivalence of the two alternative variables sets.
• Physically relevant quantities admit NC corrections which matches existing literature.

We consider the Landau system in a canonically noncommutative phase-space. A set of generalized transformations containing scaling parameters is derived which maps the NC problem to an equivalent commutative problem. The energy spectrum admits NC corrections which are computed using the explicit NC variables as well as the commutative-equivalent variables. Their exact matching solidifies the evidence of the equivalence of the two approaches. We also obtain the magnetic length and level degeneracy, which admit NC corrections. We further study the Aharonov–Bohm effect where the phase-shift is found to alter due to noncommutativity and also depends on the scaling parameters.