  We construct the states of maximal localization taking into account a
modification of the commutation relation between position and momentum
operators to all orders of the minimum length parameter. To first order, the
algebra we use reproduces the one proposed by Kempft, Mangano and Mann. It is
emphasized that a minimal length acts as a natural regulator for the theory,
thus eliminating the otherwise ever appearing infinities. So, we use our
results to calculate the first correction to the Casimir Effect due to the
minimal length. We also discuss some of the physical consequences of the
existence of a minimal length, culminating in a proposal to reformulate the
very concept of "position measurement".
