



Volume 5, Issue 1, Article 4 






On the HeisenbergPauliWeyl Inequality



Authors: 
John Michael Rassias, 



Keywords:

Pascal Identity, PlancherelParsevalRayleigh Identity, Lagrange Identity, Gaussian function, Fourier transform, Moment, Bessel equation, Hermite polynomials, HeisenbergPauliWeyl Inequality. 



Date Received:

02/01/03 



Date Accepted:

04/03/03 



Subject Codes: 
Primary: 26Xxx; Secondary: 42Xxx, 60Xxx,




Editors: 
Alexander G. Babenko, 









Abstract: 
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 aforementioned result to the higher moments for functions and establish the HeisenbergPauliWeyl inequality.
















