The aim of this book is to explain the basic concepts and phenomena of quantum. To prepare a wave packet which is localized to a region of space, we must superpose components of di. Duchkov, anton and romanenko, alexey seg 2011 annual meeting in seg technical program expanded abstracts 2011. 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 perturbation of coherent wavepacket dynamics by atom. The wave packet is decomposed in the corresponding basis of v m 4. Synchrosqueezed wave packet transforms and di eomorphism based spectral analysis for 1d general mode decompositions haizhao yang department of mathematics, stanford university october 20. That a packet distorts or not in evolution depends on whether or. Pdf synchrosqueezed wave packet transform for 2d mode. An implementation for r can be found in the wavethresh package.
The wave function of a wave packet is effectively zero everywhere except in a region of size 2 x. We note that results which are similar in spirit are independently obtained in ongoing work of smith using a di. Reasonable to expect particle to be found in region where wave function is largest in magnitude. Wave packet decomposition algorithm we briey recapitulate the wave packet decomposition algorithm described in details in duchkov et al. If the dft is computed on tico data, which includes 39,578 samples, the dft will decompose the sound into 0. Note that the wavepacket does not change its shape as time passes if all the components have the same phase velocity. As the number of waves increases, the wave packet becomes more localized in space. Physics of light and optics justin peatross michael ware brigham young university august 14, 2008. In preparation are a textbook holschneider 1991, a course dau bechies 1991, three. Wave packets lippmann schwinger equation wave packets at early times spread of wave packet 7.
Free particle motion in three dimensions springerlink. The word wavelet originates from a combination of wave and the french word for. Pdf 3d wavepacket decomposition implemented on gpus. Photon wave functions, wavepacket quantization of light, and coherence theory 3 wave packets introduced by titulaer and glauber tg 7. Pdf features of wavelet packet decomposition and discrete.
The perturbation of coherent wavepacket dynamics by atommolecule collisions. A very short introduction to sound analysis for those who. Acknowledgments this document is mostly based on my reading of the excellent book by gri. This paper introduces the synchrosqueezed wave packet transform as a method for analyzing 2d images. We have used discrete wavelet transform and wavelet packet decomposition. Inlet conditions for wave packet models in turbulent jets. Ii 39 there are two notions of schwartz class function which we must dis tinguish in the infinite center case. Pdf time domain signal analysis using wavelet packet. Christoph thiele the concept of wave packet analysis originates in carlesons famous proof of almost everywhere convergence of fourier series of lsuperscript 2 functions.
This process is experimental and the keywords may be updated as the learning algorithm improves. Photon wave functions, wavepacket quantization of light, and coherence theory 11. It focuses primarily on the wave and ray descriptions of light, but also includes a brief intro. Wavepacket decomposition for acoustic target recognition. For arbitrary wave packets, does change the shape of packets. For 5 e z we write cf gz, 0 and l2 gz, 5 to denote functions on g which satisfy. The acoustic response scattered by an object depends on its physical shape and structure and on its elastic properties. I have learned a great deal by poring over millers book. The rst sine function will have a frequency w 1 f sn 2205039578 0. Spherical harmonics as eigenfunctions of angular momentum. 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. It includes a concise summary of the material of gri. Elm waves are also particles what if traditional particles.
This is equivalent to the frequency resolution f of the decomposition. 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. Let 2 be a subgroup of the center of g with kz compact. Up is onetoone from p into g, where g is given by 1. We will also consider variants of the discrete wave packet systems obtained by using a larger collection of translations and an appropriate renormalization of the generators. An implementation of wavelet packet decomposition can be found in matlab wavelet toolbox. This tradeoff between spread in position and spread in momentum is a characteristic feature of the heisenberg uncertainty principle, and will be illustrated below. There is no warranty for correctness, please contact me if you spot a mistake. 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. H a packet in free space does not mean it is free of distortion. The wave packet propagation using wavelets sciencedirect. This transform is a combination of wave packet transforms of a certain geometric scaling, a.
The picture book of quantum mechanics springerlink. 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. This wave packet provides information about both the location and momentum of the object. The wavelet packet method is a generalization of wavelet decomposition that offers a richer signal analysis. This allows for the similar processing of 3d seismic gathers.
Photon wave functions, wavepacket quantization of light. The dispersion of the wave packet is apparent through the growth of the sphere with time. Preface this book provides an introduction to the eld of optics from a physics perspective. Since wavelet packet decomposition can provide more precise frequency. 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. As in the planewave case the wave packet travels to the right for. Wavelet packet atoms are waveforms indexed by three naturally interpreted parameters. Moreover, the narrower the spatial wave packet, and therefore the better localized the position of the wave packet, the larger the spread in the momentum of the wave. Originally known as optimal subband tree structuring sbts also called wavelet packet. Decomposition of seismic data into wavepacket representations has been successfully used for 2d data compression, interpolation and denoising. However, it cannot give us exact values for either. The time evolution of a wave function is in fact effectively governed by. This paper addresses the exploitation of the information contained in the scattered waves and with the aim of providing a broader view of waveform analysis as applied to target detection and classification applications.
Perform wavelet shrinkage using dataanalytic, hybrid sure, manual, sure. 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. The wave packet ought to behave in some way like its associated particle e. 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. 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. Pdf this paper explains a study conducted based on wavelet based transform techniques. Wave packets september, 2000 4 formation of a wave packet by superposition of two different waves of slightly different frequencies. The decomposition with these nonorthogonal frames then becomes optimal and unique. Alternatively, the gaussian is at half its maximal value at x 1. Performs wavelet decomposition on the empirical scaling function coefficients of the. This paper explains a study conducted based on wavelet packet transform. For a function that is a superposition of several wave like components.
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