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A quantum mechanical analogue of the classically chaotic triple-well oscillator under the influence of an external field and parametric excitation has been studied by using the quantum theory of motion. The on the fly calculations show the correspondence between some dynamical aspects of the classical and quantum oscillators along with a strictly quantum mechanical behaviour in case of diffusion and tunneling. Suitable external conditions have been obtained which can either assist or suppress the movement of quantum particles from one well to another. Quantum interference effects play a critical role in determining the nature of the quantum dynamics and in the presence of strong coupling to the external forces, quantum interference effects reduce drastically leading to decoherence of the quantum wave packet. In such situations, quantum dynamical features qualitatively resemble the corresponding classical dynamical behaviour and a correspondence between classical and quantum dynamics is obtained.