Sharper $N$-D Heisenberg's Uncertainty Principle
Zhichao Zhang, Xi-Ya Shi, An-Yang Wu, Dong Li
Abstract
A sharper uncertainty inequality which exhibits a lower bound tighter than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained. The condition that reaches an equality relation of the uncertainty inequality is deduced. Example and simulations are carried out to illustrate that the newly derived uncertainty principle is truly sharper than the classical one. The new proposal's applications in time-frequency analysis, optical signal processing and physical optics propagation are also given.
Topics & Concepts
Uncertainty principleMathematicsEntropic uncertaintyUpper and lower boundsGeometrical opticsSignal processingApplied mathematicsPhysicsMathematical analysisQuantum mechanicsComputer scienceTelecommunicationsQuantumRadarMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsSparse and Compressive Sensing Techniques