Download or read book Introduction to Classical and Quantum Harmonic Oscillators written by S. C. Bloch and published by Wiley-Interscience. This book was released on 1997-02-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Introduction to Classical and Quantum Harmonic Oscillators written by S. C. Bloch and published by John Wiley & Sons. This book was released on 2013-03-29 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book University Physics written by OpenStax and published by . This book was released on 2016-11-04 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. The text and images in this textbook are grayscale.

Download or read book Classical Mechanics and Quantum Mechanics An Historic Axiomatic Approach written by Peter Enders and published by Bentham Science Publishers. This book was released on 2019-09-05 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique textbook presents a novel, axiomatic pedagogical path from classical to quantum physics. Readers are introduced to the description of classical mechanics, which rests on Euler’s and Helmholtz’s rather than Newton’s or Hamilton’s representations. Special attention is given to the common attributes rather than to the differences between classical and quantum mechanics. Readers will also learn about Schrödinger’s forgotten demands on quantization, his equation, Einstein’s idea of ‘quantization as selection problem’. The Schrödinger equation is derived without any assumptions about the nature of quantum systems, such as interference and superposition, or the existence of a quantum of action, h. The use of the classical expressions for the potential and kinetic energies within quantum physics is justified. Key features: · Presents extensive reference to original texts. · Includes many details that do not enter contemporary representations of classical mechanics, although these details are essential for understanding quantum physics. · Contains a simple level of mathematics which is seldom higher than that of the common (Riemannian) integral. · Brings information about important scientists · Carefully introduces basic equations, notations and quantities in simple steps This book addresses the needs of physics students, teachers and historians with its simple easy to understand presentation and comprehensive approach to both classical and quantum mechanics..

Download or read book Classical and Quantum Mechanics of the Damped Harmonic Oscillator written by Hans Dekker (fizyka) and published by . This book was released on 1981 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The One Dimensional Harmonic Oscillator written by Timothy Luke Brown and published by . This book was released on 1998 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Theory of Non Commutative Harmonic Oscillators An Introduction written by Alberto Parmeggiani and published by Springer Science & Business Media. This book was released on 2010-04-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Classical and Quantum Dynamics written by Walter Dittrich and published by Springer Nature. This book was released on 2020-02-06 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students seeking to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger’s source theory treatment of the low-energy π-ρ-N physics and general relativity, where Riemann’s (Einstein’s) ideas on space and time and their philosophical implications are discussed.

Download or read book Workshop on Harmonic Oscillators written by D. Han and published by . This book was released on 1993 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Oscillators written by Yilun Shang and published by . This book was released on 2019 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Classical and Quantum Mechanics of the Damped Harmonic Oscillator written by H. Dekker and published by . This book was released on 1981 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book From Classical to Quantum Mechanics written by Giampiero Esposito and published by Cambridge University Press. This book was released on 2004-03-11 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.

Download or read book Harmonic Oscillator written by Moshinsky and published by CRC Press. This book was released on 1996-05-01 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Classical and Quantum Mechanics of the Damped Harmonic Oscillator written by Hans Dekker and published by . This book was released on 1981 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Oscillator Representation in Quantum Physics written by M. Dineykhan and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation ofmost problems of quantum physics leads to the solution of the Schrodinger equation with an appropriate interaction Hamiltonian or potential. However, the exact solutions are known for rather a restricted set of potentials, so that the standard eternal problem that faces us is to find the best effective approximation to the exact solution of the Schrodinger equation under consideration. In the most general form, this problem can be formulated as follows. Let a total Hamiltonian H describing a relativistic (quantum field theory) or a nonrelativistic (quantum mechanics) system be given. Our problem is to solve the Schrodinger equation Hlft = Enlftn, n i. e. , to find the energy spectrum {En} and the proper wave functions {lft } n including the'ground state or vacuum lft = 10). The main idea of any ap o proximation technique is to find a decomposition in such a way that Ha describes our physical system in the "closest to H" manner, and the Schrodinger equation HolJt. (O) = E(O)lJt. (O) n n n can be solved exactly. The interaction Hamiltonian HI is supposed to give small corrections to the zero approximation which can be calculated. In this book, we shall consider the problem of a strong coupling regime in quantum field theory, calculations ofpath or functional integrals over the Gaussian measure and spectral problems in quantum mechanics. Let us con sider these problems briefly.

Download or read book Classical and Quantum Parametric Phenomena written by Oded Zilberberg and published by Oxford University Press. This book was released on 2023-09-26 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical and Quantum Parametric Phenomena provides an overview of the phenomena arising when parametric pumping is applied to oscillators. These phenomena include parametric amplification, noise squeezing, spontaneous symmetry breaking, activated switching, cat states, and synthetic Ising spin lattices. To understand these effects, topics are introduced such as nonlinear and stochastic dynamics, coupled systems, and quantum mechanics. Throughout the book, introductions are succinct as possible and attention is focused on understanding parametric oscillators. As a result, the text helps readers to familiarize themselves with many aspects of parametric systems and understand the common theoretical origin of nanomechanical sensors, optical amplifiers, and superconducting qubits. Parametric phenomena have enabled important scientific breakthroughs over the last decades and are still at the focus of intense research efforts. This book provides a resource for experimental and theoretical physicists entering the field or wishing to gain a deeper understanding of the underlying connections. This includes combining formal and intuitive explanations, accompanied by exercises based on numerical Python codes. This combination allows readers to experience parametric phenomena from various directions and apply their understanding directly to their own projects.

Download or read book Classical And Quantum Dissipative Systems Second Edition written by Mohsen Razavy and published by World Scientific. This book was released on 2017-02-27 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potential models of nuclear reactions are considered and solved.