Entropic uncertainty relation for power-law wave packets

Abstract

For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the Heisenberg-type formulation, since it involves only the finite quantities. It is found that the total amount of entropic uncertainty converges to its lower bound in the limit of a large value of the exponent.