The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions are specified. Such variable pairs are known as complementary variables or canonically conjugate variables and, depending on interpretation, the uncertainty principle limits to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value. In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions. Optik 272: 170213.Wikipedia Rate this definition: 0.0 / 0 votes Wigner distribution and associated uncertainty principles in the framework of octonion linear canonical transform. Mathematical Methods in the Applied Sciences 46 (8): 8478–8495.ĭar, A.H., and M.Y. The two‐sided short‐time quaternionic offset linear canonical transform and associated convolution and correlation. ![]() Scaled ambiguity function and scaled Wigner distribution for LCT signals. ![]() International Journal of Wavelets Multiresolution and Information Processing 21 (01).ĭar, A.H., and M.Y. Until the dawn of quantum mechanics, it was held as a fact that all variables of an object could be known to exact precision simultaneously for a given moment. Quaternion linear canonical S -transform and associated uncertainty principles. The Heisenberg Uncertainty Principle is a fundamental theory in quantum mechanics that defines why a scientist cannot measure multiple quantum variables simultaneously. e-Prime - Advances in Electrical Engineering Electronics and Energy 4: 100162.īhat, M.Y., and A.H. Quadratic phase S-Transform: Properties and uncertainty principles. The Journal of Analysis.īhat, M.Y., and A.H. Quaternion offset linear canonical transform in one-dimensional setting. International Journal of Wavelets, Multiresolution and Information Processing 2150030.īhat, M.Y., and A.H. Wavelet packets associated with linear canonical transform on spectrum. Advances in Operator Theory 6 (68).īhat, M.Y., and A.H. Multiresolution analysis for linear canonical S transform. Integral Transforms and Special Functions 24: 401–409.īhat, M.Y., and A.H. A general form of Heisenberg-Pauli-Weyl uncertainty inequality for the Dunkel transform. Pacific Journal of Mathematics 235: 289–296. Heisenberg uncertainty principle on Chébli-Trimèche hypergroups. Proceedings of the American Mathematical Society 127: 183–194. An uncertainty principle for Hankel transforms. Continuous Wavelet Transform Involving Linear Canonical Transform. Wavelet Transforms and Their Applications, Birkhäuser: F.A. There is likewise a minimum for the product of the uncertainties of the energy and time. There is a minimum for the product of the uncertainties of these two measurements. Open Journal of Mathematical Analysis.ĭebnath, L. The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision. A variety of uncertainty principles for the Hankel-Stockwell transform. Journal of Pseudo-Differential Operators and Applications 11 (2): 543–563. Uncertainty principles for the Hankel-Stockwell transform. Integral Transforms and Special Functions 18 (5): 369–381. Uncertainty principles for the Hankel transform. Integral Transforms and Special Functions 22 (9): 655–670. Logarithmic uncertainty principle for the Hankel transform. SIAM Journal on Mathematical Analysis 2 (4): 601–606. Uncertainty inequalities for Hankel transforms. Some important fractional transformations for signal processing. Numerical modeling of cylindrically symmetric nonlinear self-focusing using an adaptive fast Hankel split-step method. ![]() Bulletin of the Australian Mathematical Society 59 (3): 353–360.īanerjee, P.P., G. An uncertainty principle for the Dunkl transform. Some results for the windowed Fourier transform related to the spherical mean operator. That is, the more exactly the position is determined, the less known the momentum, and vice versa. Journal of Pseudo-Differential Operators and Applications 9 (3): 573–587. The Heisenberg uncertainty principle states that it is impossible to know simultaneously the exact position and momentum of a particle. Uncertainty principles for spherical mean \(L^2\)-multiplier operators. Journal of Mathematical Physics 24 (7): 1711–1713. Inequalities and local uncertainty principles. SIAM Journal on Mathematical Analysis 15 (1): 151–164. Bandwidth versus time concentration: the Heisenberg-Pauli-Weyl inequality.
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