The quantum mechanical effects has wide applications in quantum plasma echoes, quantum plasma instabilities and microelectronics devices. Quantum effects may become important when the electron number density of the order of 10~(30) m~(-3) and small temperatures of a few thousand Kelvin. A dusty plasma is a three-component plasma consisting of electrons, ions, and a solid grains. We use the quantum hydrodynamic model to derive the plasma dispersion equation to study the growth rate of electron drift waves in quantum dusty plasmas. The growth shows depends on the electron temperature, electron density, electron drift velocity and wave number, ions and dust mass. The results may be useful to understand the physics of dense astrophysical objects. Different approximations are tried to solve the dispersion equation.
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