scholarly journals The N-Dimensional Uncertainty Principle for the Free Metaplectic Transformation

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1685
Author(s):  
Rui Jing ◽  
Bei Liu ◽  
Rui Li ◽  
Rui Liu
Keyword(s):  
Fourier Transform ◽  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Transformation Operator ◽  
Local Analysis ◽  
Transform Domain ◽  
Uncertainty Principles ◽  
The Fourier Transform ◽  
Heisenberg's Uncertainty Principle ◽  
Fourier Transform Domain

The free metaplectic transformation is an N-dimensional linear canonical transformation. This transformation operator is useful, especially for signal processing applications. In this paper, in order to characterize simultaneously local analysis of a function (or signal) and its free metaplectic transformation, we extend some different uncertainty principles (UP) from quantum mechanics including Classical Heisenberg’s uncertainty principle, Nazarov’s UP, Donoho and Stark’s UP, Hardy’s UP, Beurling’s UP, Logarithmic UP, and Entropic UP, which have already been well studied in the Fourier transform domain.

scholarly journals Hoe zeker is Heisenbergs onzekerheidsprincipe?

2021 ◽  
Vol 113 (1) ◽  
pp. 137-156
Author(s):  
Jeanne Peijnenburg ◽  
David Atkinson
Keyword(s):  
Quantum Mechanics ◽  
Recent Work ◽  
Uncertainty Principle ◽  
Copenhagen Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Uncertainty Principles ◽  
Werner Heisenberg ◽  
Heisenberg's Uncertainty Principle

Abstract How certain is Heisenberg’s uncertainty principle?Heisenberg’s uncertainty principle is at the heart of the orthodox or Copenhagen interpretation of quantum mechanics. We first sketch the history that led up to the formulation of the principle. Then we recall that there are in fact two uncertainty principles, both dating from 1927, one by Werner Heisenberg and one by Earle Kennard. Finally, we explain that recent work in physics gives reason to believe that the principle of Heisenberg is invalid, while that of Kennard still stands.

scholarly journals Wave splitting for first-order systems of equations

2002 ◽  
Vol 32 (6) ◽  
pp. 371-381 ◽  
Author(s):  
G. Caviglia ◽  
A. Morro
Keyword(s):  
Fourier Transform ◽  
Partial Differential Equations ◽  
Time Domain ◽  
Space Variable ◽  
Transform Domain ◽  
Systems Of Equations ◽  
First Order ◽  
Wave Splitting ◽  
The Fourier Transform ◽  
Fourier Transform Domain

Systems of first-order partial differential equations are considered and the possible decomposition of the solutions in forward and backward propagating is investigated. After a review of a customary procedure in the space-time domain (wave splitting), attention is addressed to systems in the Fourier-transform domain, thus considering frequency-dependent functions of the space variable. The characterization is given for the direction of propagation and applications are developed to some cases of physical interest.

Some shaper uncertainty principles for multivector-valued functions

2016 ◽  
Vol 14 (06) ◽  
pp. 1650043
Author(s):  
Minggang Fei ◽  
Yubin Pan ◽  
Yuan Xu
Keyword(s):  
Fourier Transform ◽  
Clifford Algebra ◽  
Uncertainty Principle ◽  
Dunkl Transform ◽  
Uncertainty Principles ◽  
Heisenberg Uncertainty Principle ◽  
Clifford Fourier Transform ◽  
Heisenberg Uncertainty ◽  
The Fourier Transform ◽  
Adjoint Operators

The Heisenberg uncertainty principle and the uncertainty principle for self-adjoint operators have been known and applied for decades. In this paper, in the framework of Clifford algebra, we establish a stronger Heisenberg–Pauli–Wely type uncertainty principle for the Fourier transform of multivector-valued functions, which generalizes the recent results about uncertainty principles of Clifford–Fourier transform. At the end, we consider another stronger uncertainty principle for the Dunkl transform of multivector-valued functions.

Seismic trace interpolation in the Fourier transform domain

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 355-369 ◽  
Author(s):  
Necati Gülünay
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Interpolation Method ◽  
Original Data ◽  
Transform Domain ◽  
3D Data ◽  
Adaptive Interpolation ◽  
Data Adaptive ◽  
The Fourier Transform ◽  
Fourier Transform Domain

A data adaptive interpolation method is designed and applied in the Fourier transform domain (f‐k or f‐kx‐ky for spatially aliased data. The method makes use of fast Fourier transforms and their cyclic properties, thereby offering a significant cost advantage over other techniques that interpolate aliased data. The algorithm designs and applies interpolation operators in the f‐k (or f‐kx‐ky domain to fill zero traces inserted in the data in the t‐x (or t‐x‐y) domain at locations where interpolated traces are needed. The interpolation operator is designed by manipulating the lower frequency components of the stretched transforms of the original data. This operator is derived assuming that it is the same operator that fills periodically zeroed traces of the original data but at the lower frequencies, and corresponds to the f‐k (or f‐kx‐ky domain version of the well‐known f‐x (or f‐x‐y) domain trace interpolators. The method is applicable to 2D and 3D data recorded sparsely in a horizontal plane. The most common prestack applications of the algorithm are common‐mid‐point domain shot interpolation, source‐receiver domain shot interpolation, and cable interpolation.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

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