On the Heisenberg-Pauli-Weyl Inequality

摘要

In 1927, W. Heisenberg demonstrated the impossibility of specifying simultaneously the position and the momentum of an electron within an atom.The following result named, Heisenberg inequality, is not actually due to Heisenberg. In 1928, according to H. Weyl this result is due to W. Pauli.The said inequality states, as follows: Assume that is a complex valued function of a random real variable such that . Then the product of the second moment of the random real for and the second moment of the random real for is at least , where is the Fourier transform of , such that and , and . In this paper we generalize the afore-mentioned result to the higher moments for functions and establish the Heisenberg-Pauli-Weyl inequality.