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![]() If you're focusing on trying to watch the speed, then you may be off a bit when measuring the exact time across the finish line, and vice versa. The physical nature of the system imposes a definite limit upon how precise this can all be. We'll see the car touch the finish line, push the stopwatch button, and look at the digital display. In this classical case, there is clearly some degree of uncertainty about this, because these actions take some physical time. We measure the speed by pushing a button on a stopwatch at the moment we see it cross the finish line and we measure the speed by looking at a digital read-out (which is not in line with watching the car, so you have to turn your head once it crosses the finish line). We are supposed to measure not only the time that it crosses the finish line but also the exact speed at which it does so. Let's say that we were watching a race car on a track and we were supposed to record when it crossed a finish line. Optik 272: 170213.Though the above may seem very strange, there's actually a decent correspondence to the way we can function in the real (that is, classical) world. 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. Quaternion linear canonical S -transform and associated uncertainty principles. 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. Later, in 1927, a German physicist called Werner Heisenberg proposed that it is not possible to know where exactly an electron is located when it behaves like a wave and what its velocity is simultaneously because by trying to take any measurements, we would be disturbing it in some way. A general form of Heisenberg-Pauli-Weyl uncertainty inequality for the Dunkel transform. Heisenberg Uncertainty Principle Definition. ![]() 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. Open Journal of Mathematical Analysis.ĭebnath, L. A variety of uncertainty principles for the Hankel-Stockwell transform. That is, the more exactly the position is determined, the less known the momentum, and vice versa. Journal of Pseudo-Differential Operators and Applications 11 (2): 543–563. The Heisenberg uncertainty principle states that it is impossible to know simultaneously the exact position and momentum of a particle. 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. Journal of Pseudo-Differential Operators and Applications 9 (3): 573–587. 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. It relates to measurements of sub-atomic particles. Bandwidth versus time concentration: the Heisenberg-Pauli-Weyl inequality. Heisenbergs uncertainty principle is one of the most important results of twentieth century physics. ![]()
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