Standard and entropic uncertainty relations of the finite well

This paper deals with the standard and entropic uncertainty relations for the finite-potential well with different length and potential depth. We calculate the position and momentum dispersions and entropies that are dependent on the quantum states of the finite well and determine the corresponding standard and entropic uncertainty relations. Then we calculate the entropy of occurrence for the mass point inside and outside the well. We discuss the results and determine a class of probability distributions with a parameter for which the standard deviation becomes infinite, independent of the value of this parameter.