In preparation are a textbook holschneider 1991, a course dau bechies 1991, three. This allows for the similar processing of 3d seismic gathers. To prepare a wave packet which is localized to a region of space, we must superpose components of di. Algorithms for evaluating the composition of this type of frame are derived from the coherence property of the given signal and image processing is used to estimate the approximate form of needed functions.
The rst sine function will have a frequency w 1 f sn 2205039578 0. The wave function for a single electron, also called a wave packet, is created by combining many wave functions with different wavelengths, where the wavelength is determined by the electrons momentum. However, it cannot give us exact values for either. Pdf features of wavelet packet decomposition and discrete. Free particle motion in three dimensions springerlink. This paper introduces the synchrosqueezed wave packet transform as a method for analyzing twodimensional images.
The perturbation of coherent wavepacket dynamics by atom. This decomposition may also be of independent interest. Reasonable to expect particle to be found in region where wave function is largest in magnitude. We have used discrete wavelet transform and wavelet packet decomposition. We note that results which are similar in spirit are independently obtained in ongoing work of smith using a di. This tradeoff between spread in position and spread in momentum is a characteristic feature of the heisenberg uncertainty principle, and will be illustrated below. The wavelet packet method is a generalization of wavelet decomposition that offers a richer signal analysis. An implementation for r can be found in the wavethresh package. H a packet in free space does not mean it is free of distortion. For arbitrary wave packets, does change the shape of packets. The picture book of quantum mechanics springerlink. The wave packet propagation using wavelets sciencedirect. Up is onetoone from p into g, where g is given by 1.
The aim of this book is to explain the basic concepts and phenomena of quantum. Wave packets lippmann schwinger equation wave packets at early times spread of wave packet 7. Alternatively, the gaussian is at half its maximal value at x 1. Wave mechanical phenomena such as resonance and interference, in both light and matter, are central to the principles of quantum coherent control over molecular processes. Perform wavelet shrinkage using dataanalytic, hybrid sure, manual, sure. Photon wave functions, wavepacket quantization of light. Duchkov, ipgg sb ras and novosibirsk state university, and fredrik andersson, lund university summary decomposition of seismic data into wave packet representations has been successfully used for 2d data compression, in. Wave packet proper orthogonal decomposition basis wave proper orthogonal decomposition mode dynamic mode decomposition these keywords were added by machine and not by the authors. There is no warranty for correctness, please contact me if you spot a mistake. The dispersion of the wave packet is apparent through the growth of the sphere with time. Duchkov, anton and romanenko, alexey seg 2011 annual meeting in seg technical program expanded abstracts 2011. Spherical harmonics as eigenfunctions of angular momentum. Preface this book provides an introduction to the eld of optics from a physics perspective.
This process is experimental and the keywords may be updated as the learning algorithm improves. The primary text book for this course is quantum mechanics for scientists and engineers by d. The acoustic response scattered by an object depends on its physical shape and structure and on its elastic properties. Pdf this paper explains a study conducted based on wavelet based transform techniques. The time evolution of a wave function is in fact effectively governed by.
A very short introduction to sound analysis for those who. Partial wave decomposition of plane wave and gaussian wave packet. As the number of waves increases, the wave packet becomes more localized in space. Laurent demanet, stanford university the new edition of this classic book gives all the major concepts.
Photon wave functions, wavepacket quantization of light, and coherence theory 11. An implementation in java for 1d and 2d wavelet packets using haar, daubechies, coiflet, and legendre. This is equivalent to the frequency resolution f of the decomposition. Wavelet packet atoms are waveforms indexed by three naturally interpreted parameters. Note that the wavepacket does not change its shape as time passes if all the components have the same phase velocity. That a packet distorts or not in evolution depends on whether or. The perturbation of coherent wavepacket dynamics by atommolecule collisions. Decomposition of seismic data into wavepacket representations has been successfully used for 2d data compression, interpolation and denoising. The wave packet is decomposed in the corresponding basis of v m 4. Performs wavelet decomposition on the empirical scaling function coefficients of the. The wave function of a wave packet is effectively zero everywhere except in a region of size 2 x. Photon wave functions, wavepacket quantization of light, and coherence theory 3 wave packets introduced by titulaer and glauber tg 7. Inlet conditions for wave packet models in turbulent jets. Synchrosqueezed wave packet transform for 2d mode decomposition haizhao yangyand lexing ying ydepartment of mathematics, the university of texas at austin department of mathematics and ices, the university of texas at austin september 2012 abstract this paper introduces the synchrosqueezed wave packet transform as a method for analyzing 2d.
This paper explains a study conducted based on wavelet packet transform. This transform is a combination of wave packet transforms of a certain geometric scaling, a reallocation technique for sharpening phase space representations, and clustering algorithms for modal decomposition. The word wavelet originates from a combination of wave and the french word for. Originally known as optimal subband tree structuring sbts also called wavelet packet. For 5 e z we write cf gz, 0 and l2 gz, 5 to denote functions on g which satisfy. The decomposition with these nonorthogonal frames then becomes optimal and unique. If the dft is computed on tico data, which includes 39,578 samples, the dft will decompose the sound into 0. An implementation of wavelet packet decomposition can be found in matlab wavelet toolbox. This paper introduces the synchrosqueezed wave packet transform as a method for analyzing 2d images. Elm waves are also particles what if traditional particles.
Physics of light and optics justin peatross michael ware brigham young university august 14, 2008. We consider representations of 3d seismic data or image ux of the form. Likewise, textbook numerical methods for the wave equation in two or three. Ii 39 there are two notions of schwartz class function which we must dis tinguish in the infinite center case. Pdf 3d wavepacket decomposition implemented on gpus. Coherence and control in photomolecular wave packet.
In this paper we present a fast implementation of a 3d wavepacket decomposition using graphical processing units gpus. The wave packet ought to behave in some way like its associated particle e. In an open system, this may be achieved using a fourier expansion. Focusing on the dynamical aspects, this dissertation is a compilation of studies on the interaction physics involving wave packets in molecules, the driving light field, and the underlying coherence and control. Wave packet decomposition algorithm we briey recapitulate the wave packet decomposition algorithm described in details in duchkov et al. Christoph thiele the concept of wave packet analysis originates in carlesons famous proof of almost everywhere convergence of fourier series of lsuperscript 2 functions. Pdf time domain signal analysis using wavelet packet. As in the planewave case the wave packet travels to the right for. Let 2 be a subgroup of the center of g with kz compact. Since wavelet packet decomposition can provide more precise frequency. I have learned a great deal by poring over millers book. Wavepacket decomposition for acoustic target recognition.
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