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In this paper, we study a two-dimensional rotationally symmetric harmonic oscillator with time-dependent frictional force. At the classical level, we solve the equations of motion for a particular case of the time-dependent coefficient of friction. At the quantum level, we use the Lewis-Riesenfeld procedure of invariants to construct exact solutions for the corresponding time-dependent Schrödinger equations. The eigenfunctions obtained are in terms of the generalized Laguerre polynomials. By means of the solutions, we verify a generalization version of Heisenberg's uncertainty relation and derive the generators of the su(1, 1) Lie algebra. Based on these generators, we construct the coherent states à la Barut-Girardello and à la Perelomov and respectively study their properties. [ABSTRACT FROM AUTHOR]

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass. [ABSTRACT FROM AUTHOR]