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Yayın Non-commutative geometry and application to schrödinger equation with certain central potentials(Maltepe Üniversitesi, 2019) Slimane, ZaiemWe obtain exact solutions of the 2D Schr¨odinger equation with the central potentials V (r) = ar2 + br?2 + cr?4 and V (r) = ar?1+br?2 in a non-commutative space up to the first order of noncommutativity parametert using the power-series expansion method similar to the 2D Schr¨odinger equation with the singular even-power and inverse-power potentials respectively in commutative space. We derive the exact non-commutative energy levels and show that the energy is shifted to m levels, as in the Zeeman effect.