Harmonic Oscillators
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Introduction To Classical And Quantum Harmonic Oscillators
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Author : S. C. Bloch
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-29
Introduction To Classical And Quantum Harmonic Oscillators written by S. C. Bloch and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-29 with Science categories.
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating concepts, key to understanding the physical universe and a linchpin in fields as diverse as mechanics, electromagnetics, electronics, optics, acoustics, and quantum mechanics. Complete with disk, Introduction to Classical and Quantum Harmonic Oscillators is a hands-on guide to understanding how harmonic oscillators function and the analytical systems used to describe them. Professionals and students in electrical engineering, mechanical engineering, physics, and chemistry will gain insight in applying these analytical techniques to even more complex systems. With the help of spreadsheets ready to run on Microsoft Excel (or easily imported to Quattro Pro or Lotus 1-2-3), users will be able to thoroughly and easily examine concepts and questions, of considerable difficulty and breadth, without painstaking calculation. The software allows users to imagine, speculate, and ask "what if .?" and then instantly see the answer. You're not only able to instantly visualize results but also to interface with data acquisition boards to import real-world information. The graphic capability of the software allows you to view your work in color and watch new results blossom as you change parameters and initial conditions. Introduction to Classical and Quantum Harmonic Oscillators is a practical, graphically enhanced excursion into the world of harmonic oscillators that lets the reader experience and understand their utility and unique contribution to scientific understanding. It also describes one of the enduring themes in scientific inquiry, begun in antiquity and with an as yet unimagined future.
Harmonic Oscillators
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Author : Yilun Shang
language : en
Publisher:
Release Date : 2019
Harmonic Oscillators written by Yilun Shang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Science categories.
"This book gathers state-of-the-art advances on harmonic oscillators including their types, functions, and applications. In Chapter 1, Neetik and Amlan have discussed the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology, etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable physical and chemical changes. The desired effect is achieved by reducing the spatial boundary from infinity to a finite region. Similarly, in the last decade, information measures were investigated extensively in diverse quantum problems, in both free and constrained situations. The most prominent amongst these are: Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy, Onicescu energy and several complexities. Arguably, these are the most effective measures of uncertainty, as they do not make any reference to some specific points of a respective Hilbert space. These have been invoked to explain several physic-chemical properties of a system under investigation. Kullback Leibler divergence or relative entropy describes how a given probability distribution shifts from a reference distribution function. This characterizes a measure of discrimination between two states. In other words, it extracts the change of information in going from one state to another. In Chapter 2, Nabakumar, Subhasree, and Paulami have revisited classical-quantum correspondence in the context of linear Simple Harmonic Oscillator (SHO). According to Bohr's correspondence principle, quantum mechanically calculated results match with the classically expected results when quantum number is very high. Classical quantum correspondence may also be visualized in the limit when the action integral is much greater than Planck's constant. When de-Broglie wave length associated with a particle is much larger than system size, then quantum mechanical results also match with the classical results. In the context of dynamics, Ehrenfest equation of motion is used in quantum domain, which is analogous to classical Newton's equation of motion. SHO is one of the most important systems for several reasons. It is one of the few exactly solvable problems. Any stable molecular potential can be approximated by SHO near the equilibrium point. This builds the foundation for the understanding of complex modes of vibration in large molecules, the motion of atoms in a solid lattice, the theory of heat capacity, vibration motion of nuclei in molecule etc. The authors have revisited the common solution techniques and important properties of both classical and quantum linear SHO. Then they focused on probability distribution, quantum mechanical tunneling, classical and quantum dynamics of position, momentum and their actuations, viral theorems, etc. and also analyzed how quantum mechanical results finally tend to classical results in the high quantum number limit. In Chapter 3, Neeraj has discussed the nature of atomic motions, sometimes referred to as lattice vibrations. The lattice dynamics deals with the vibrations of the atoms inside the crystals. In order to write the dynamic equations of the motion of crystal atoms, we need to describe an inter-atomic interaction. Therefore, it is natural to start the study of the lattice dynamics with the case of small harmonic vibrations. The dynamics of one-dimensional and two-dimensional vibrations of monatomic and diatomic crystals can be understood by using the simple model forces based on harmonic approximation. This harmonic approximation is related to a simple ball-spring model. According to this model, each atom is coupled with the neighboring atoms by spring constants. The collective motion of atoms leads to a distinct traveling wave over the whole crystal, leading to the collective motion, so-called phonon. The simple ball-spring model enlightens us some of the significant common features of lattice dynamics that have been discussed throughout this chapter. Further, this chapter helps in understanding the quantization energy of a harmonic oscillation and the concept of phonon"--
Second International Workshop On Harmonic Oscillators
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Author :
language : en
Publisher:
Release Date : 1995
Second International Workshop On Harmonic Oscillators written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Workshop On Harmonic Oscillators
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Author : D. Han
language : en
Publisher:
Release Date : 1993
Workshop On Harmonic Oscillators written by D. Han and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Harmonic oscillators categories.
Harmonic Oscillator
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Author : Moshinsky
language : en
Publisher: CRC Press
Release Date : 1996-05-01
Harmonic Oscillator written by Moshinsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-01 with Technology & Engineering categories.
A detailed introduction to the principles of particle detectors used in physics, biology, and medicine. Introductory chapters review the interactions of particles and radiation with matter, introduce the principles of detector operation and describe different types of measurement. The main body of the book describes all currently used detectors and counters, including their basic principles, potential uses and limitations. Two chapters are dedicated to electronics (readout methods, monitoring, data acquisition) and data analysis. A final chapter gives examples of detector systems. Concludes with a glossary of terms, tables of units and physical constants, and a reference list. Annotation copyrighted by Book News, Inc., Portland, OR
Structured Electronic Design
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Author : Arie van Staveren
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Structured Electronic Design written by Arie van Staveren and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Technology & Engineering categories.
Analog design still has, unfortunately, a flavor of art. Art can be beautiful. However, art in itself is difficult to teach to students and difficult to transfer from experienced analog designers to new trainee designers in companies. Structured Electronic Design: High-Performance Harmonic Oscillators and Bandgap References aims to systemize analog design. The use of orthogonalization of the design of the fundamental quality aspects (noise, distortion, and bandwidth) and hierarchy in the subsequent design steps, enables designers to achieve high-performance designs, in a relatively short time. As a result of the systematic design procedure, the effect of design decisions on the circuit performance is made clear. Additionally, the use of resources for reaching a specified performance is tracked. This book, therefore, describes the structured electronic design of high-performance harmonic oscillators and bandgap references. The structured design of harmonic oscillators includes the maximization of the carrier-to- noise ratio by means of tapping, i.e. an impedance adaption method for noise matching. The bandgap reference, a popular implementation of a voltage reference, is studied via the unusual concept of the linear combination of base-emitter voltages. The presented method leads to the design of high-performance references in CMOS and Bipolar technology. Using this concept, on a high level of abstraction the quality with respect to, for instance, noise and power-supply rejection can be identified. In this book, it is shown with several design examples that this method provides an excellent starting point for the design of high-performance bandgap references. Auxiliary to the harmonic-oscillator and bandgap reference design are the negative- feedback amplifiers. In this book the systematic design of the dynamic behavior is emphasized. By means of the identification of the dominant poles, it is possible to give an upper limit of the attainable bandwidth, even before the real frequency compensation is accomplished. Structured Electronic Design: High-Performance Harmonic Oscillators and Bandgap References is a valuable book for researchers and designers, as well as students in the field of analog design. It helps both the experienced and trainee designer to come to grips with the design of analog circuits. The presented method is illustrated by several well- described design examples.
Harmonic Oscillators And Two By Two Matrices In Symmetry Problems In Physics
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Author : Young Suh Kim
language : en
Publisher: MDPI
Release Date : 2018-07-09
Harmonic Oscillators And Two By Two Matrices In Symmetry Problems In Physics written by Young Suh Kim and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Electronic book categories.
This book is a printed edition of the Special Issue "Harmonic Oscillators In Modern Physics" that was published in Symmetry
Design Of Crystal And Other Harmonic Oscillators
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Author : Benjamin Parzen
language : en
Publisher:
Release Date :
Design Of Crystal And Other Harmonic Oscillators written by Benjamin Parzen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction
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Author : Alberto Parmeggiani
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-22
Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction written by Alberto Parmeggiani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Mathematics categories.
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Oscillators And Oscillatory Signals From Smooth To Discontinuous
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Author : Valery N. Pilipchuk
language : en
Publisher: Springer Nature
Release Date : 2023-09-23
Oscillators And Oscillatory Signals From Smooth To Discontinuous written by Valery N. Pilipchuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-23 with Science categories.
This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford’s algebras, give rise to the essentially nonlinear “quasi-impact” methodology based on the idea of non-smooth temporal substitutions. In the years since “Nonlinear Dynamics: Between Linear and Impact Limits,” the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation j2 =± 1. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools.