



Volume 6, Issue 1, Article 11 






On the HeisenbergWeyl Inequality



Authors: 
John Michael Rassias, 



Keywords:

HeisenbergWeyl Inequality, Uncertainty Principle, Absolute Moment, Gaussian, Extremum Principle. 



Date Received:

20/09/04 



Date Accepted:

25/11/04 



Subject Codes: 
26Dxx, 30Xxx, 33Xxx, 42Xxx, 43Xxx, 60Xxx




Editors: 
George Anastassiou, 









Abstract: 
In 1927, W. Heisenberg demonstrated the impossibility of specifying simultaneously the position and the momentum of an electron within an atom.The wellknown second moment HeisenbergWeyl inequality states: 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 2004, the author generalized the aforementioned result to the higher order absolute moments for functions with orders of moments in the set of natural numbers . In this paper, a new generalization proof is established with orders of absolute moments in the set of nonnegative real numbers. Afterwards, an application is provided by means of the wellknown Euler gamma function and the Gaussian function and an open problem is proposed on some pertinent extremum principle. This inequality can be applied in harmonic analysis and quantum mechanics.
















