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In this paper we have obtained the exact eigenstates of a two dimensionaldamped harmonic oscillator in the presence of an external magnetic fieldvarying with respect to time in time dependent noncommutative space. It hasbeen observed that for some specific choices of the damping factor, the timedependent frequency of the oscillator and the time dependent external magneticfield, there exists interesting solutions of the time dependent noncommutativeparameters following from the solutions of the Ermakov-Pinney equation.Further, these solutions enable us to get exact analytic forms for the phasewhich relates the eigenstates of the Hamiltonian with the eigenstates of theLewis invariant. Then we compute the expectation value of the Hamiltonian. Theexpectation values of the energy are found to vary with time for differentsolutions of the Ermakov-Pinney equation corresponding to different choices ofthe damping factor, the time dependent frequency of the oscillator and the timedependent applied magnetic field. We also compare our results with those in theabsence of the magnetic field obtained earlier.

Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space