We construct the generalized uncertainty principle and the minimum uncertainty states using a one-dimensional quantum mechanical model which involves discrete coordinate space. To this end, we compactify momentum space that results in the discrete coordinate space. We find that it involves the usual Heisenberg uncertainty principle with modification terms suppressed by various powers of the momentum operator and the terms like &langpn&rang where n is an integer. Next, we extend our result to quantum mechanics with discrete phase space which results from compactifying both coordinate and momentum spaces. Further, we investigate the time evolution of minimum uncertainty state wave packets in discrete quantum phase space. We find that minimum wave packets exhibit revival dynamics due to the discreteness of phase space.
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