Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders

Understand

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.