Introduction to Classical and Quantum Harmonic Oscillators.

By: Bloch, Sylvan CPublisher: Hoboken : John Wiley & Sons, Incorporated, 1997Copyright date: ©2013Edition: 2nd edDescription: 1 online resource (653 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781118710821Subject(s): Electromagnetics.;Harmonic oscillators.;ScienceGenre/Form: Electronic books. Additional physical formats: Print version:: Introduction to Classical and Quantum Harmonic OscillatorsDDC classification: 530.4/16 LOC classification: QC125.2 .B384 2013Online resources: Click to View
Contents:
Cover -- Half Title page -- Title page -- Copyright page -- Dedication -- Preface -- Chapter 1: Classical Perspective -- 1.1 Importance of the Harmonic Oscillator -- 1.2 Newtonian Perspective -- 1.3 Restoring Force -- 1.4 Free Harmonic Oscillator -- 1.5 LC Resonator -- 1.6 Journey Through the Center of the Earth -- 1.7 Low Satellite Orbit -- 1.8 FREE-OSC, Free Oscillator Worksheet -- 1.9 Phase Space, Part 1 -- 1.10 PHASE-SP, Phase Space Worksheet -- 1.11 Callisto, Galileo, and French -- 1.12 Searching for Planets -- 1.13 Franklin, Priestly, Verne, and Burroughs -- What's Next? -- Chapter 2: Oscillator Energy -- 2.1 Conservative Forces -- 2.2 Potential Energy -- 2.3 Kinetic Energy -- 2.4 Conservation of Energy -- 2.5 Phase Space, Part 2 -- 2.6 Energy Diagrams -- 2.7 Equipartition of Energy -- 2.8 General Potential Energy Function -- 2.9 Perturbed Satellite Orbit -- 2.10 High Power-Law Oscillators -- 2.11 Adiabatic Invariance -- 2.12 UNDAMPED, Free Oscillator Energy Worksheet -- 2.13 Bungee Jumpers Beware -- 2.14 Summary -- Chapter 3: Damped Oscillators -- 3.1 Velocity-Dependent Resistive Force -- 3.2 FORCE-RV, Resistive Force Worksheet -- 3.3 Restoring Force and Resistive Force -- 3.4 Under-Damped Oscillator -- 3.5 Critically Damped Oscillator -- 3.6 Over-Damped Oscillator -- 3.7 Summary of Free, Damped Oscillators -- What's Next? -- Chapter 4: Forced Oscillators -- 4.1 Forced Free Mass -- 4.2 Forced Damped Mass -- 4.3 General Solution for Forced Damped Mass -- 4.4 Power Transfer -- 4.5 Forced Damped Oscillator -- 4.6 Permittivity for Bound Charges -- 4.7 FORCEOSC, Forced Oscillator Worksheet -- 4.8 Summary -- What's Next? -- Chapter 5: Q, R, X, Y, and Z -- 5.1 What Is Q? -- 5.2 Frequency Domain -- 5.3 Time Domain -- 5.4 Q of Various Oscillators -- 5.6 Resonant Detection, Mössbauer Effect -- 5.7 Q Multipliers and Dividers -- 5.8 Q Switches.
5.9 Classical Uncertainty Principle, Part 1 -- 5.10 ABC-OF-Q, Worksheet in Time and Frequency -- 5.11 Impedance and Admittance -- 5.12 Impedance and Admittance: Damped Mass -- 5.13 Impedance and Admittance: Harmonic Oscillator -- 5.14 Y-AND-Z, Admittance and Impedance Worksheet -- 5.15 How Henry Cavendish Weighed Planet Earth -- What's Next? -- Chapter 6: Fourier Perspective -- 6.1 Signal Classification -- 6.2 Periodic Signals -- 6.3 Oscillator with Periodic Force -- 6.4 Bandwidth and Spectral Density -- 6.5 Laplace's Equation -- 6.6 Non-Periodic Signals -- 6.7 Classical Uncertainty Principle, Part 2 -- 6.8 Alternative Formats -- 6.9 Laplace Transform -- 6.10 Hilbert Transform -- 6.11 Parseval's Theorem -- 6.12 Joint Time-Frequency Analysis -- 6.13 Inductive Leap -- What's Next? -- Chapter 7: Elements of Linear Systems -- 7.1 What Is a Linear System? -- 7.2 Ode to the Sinusoid -- 7.3 Fast Fourier Transform -- 7.4 Test Signals -- 7.5 Step Function Response -- 7.6 Impulse Response -- 7.7 Frequency Domain Response Using Phasors -- 7.8 Impulse Response and Causality -- 7.9 System Function via Fourier Transform -- 7.10 Impulse Response via Fourier Transform -- 7.11 Convolution -- 7.12 Power Spectral Density -- 7.13 Wiener-Khintchine Theorem -- 7.14 Auto- and Cross-Correlation Functions -- 7.15 Coherence Function -- 7.16 System Identification -- 7.17 Deconvolution -- 7.18 Data Windows -- 7.19 Central Limit Theorem -- What's Next? -- Chapter 8: Methods of Advanced Dynamics -- 8.1 Generalized Coordinates -- 8.2 Generalized Momenta -- 8.3 Lagrange's Equations -- 8.4 Hamilton's Equations -- 8.5 Poisson Brackets -- 8.6 Hamilton's Principle -- 8.7 Hamilton-Jacobi Equation -- 8.8 Symmetry of the Hamiltonian Function -- What's Next? -- Chapter 9: Coupled Oscillators -- 9.1 Two Coupled Oscillators -- 9.2 Magnetically Coupled Resonators.
9.3 COUPLOSC, Worksheet for Coupled Oscillators -- 9.4 Time Evolution, Weak Coupling -- 9.5 COUPLOS2, Worksheet #2 for Coupled Oscillators -- 9.6 Normal Coordinates -- 9.7 Oscillating Galaxies -- 9.8 Synchronized Oscillators -- What's Next? -- Chapter 10: Statistical Perspective -- 10.1 Distributions and Moments -- 10.2 Accuracy and Precision -- 10.3 Parable of the Bunny Rabbits -- 10.4 Displacement Probability Density -- 10.5 Uncertainty Due to Thermal Motion -- 10.6 More Distribution Functions -- 10.7 Natural Sources of Randomness -- 10.8 Poisson, Exponential, and Gaussian Distributions -- 10.9 Random Excitation -- 10.10 Entropy -- 10.11 Virial Theorem -- 10.12 Liouville's Theorem -- 10.13 Information and Noise -- 10.14 Stochastic Resonance -- 10.15 Phase Space Correlation and Covariance -- 10.16 Predictability -- 10.17 Time Evolution and Predictions -- 10.18 Expectation Values: Caveat Emptor -- 10.19 Expert Opinions on Predictability and Causality -- What's Next? -- Chapter 11: Quantum Perspective -- 11.1 Classical Crisis -- 11.2 A Collection of Oscillators -- 11.3 PLANCK, Worksheet for Blackbody Radiation -- 11.4 Harmonic Oscillators and Radiation -- 11.5 Wilson-Sommerfeld-Ishiwara Quantization Rule -- 11.6 Summary of Energy Level Spacing -- 11.7 Quantization of Angular Momentum -- What's Next? -- Chapter 12: Quantum Oscillators -- 12.1 Wave-Like Property of Momentum -- 12.2 Schrödinger Equation -- 12.3 Dynamic Variables and Their Operators -- 12.4 Free Particle -- 12.5 A Particle in a Box -- 12.6 Superposition of States -- 12.7 Electric Dipole Radiation -- 12.8 Dipole Transitions, Particle in a Box -- 12.10 Harmonic Oscillator -- 12.11 Harmonic Oscillator Dipole Transitions -- 12.12 QUANTOSC, Quantum Oscillator Worksheet -- 12.13 Revival of Wavefunctions -- 12.14 Discovery of Classical Oscillators -- 12.15 Meanwhile, Back in Heligoland ….
12.16 Single-Electron Oscillator -- 12.17 Trouble in Paradise -- What's Next? -- Appendix 1: Worksheets -- Installing the Files from the Diskette -- Useful Spreadsheet Functions -- Appendix 2: The Hilbert Transform -- A2.1 Derivation via Unit Step -- A2.2 Constructing an Analytic Function -- A2.3 Fourier Transform of Unit Step -- A2.4 Application of the Hilbert Transform -- A2.6 References for the Hilbert Transform -- Bibliography -- Books -- Software -- Selected Papers from American Journal of Physics -- Selected Papers from Other Journals -- Index.
Summary: 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 HarmonicSummary: 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.
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Cover -- Half Title page -- Title page -- Copyright page -- Dedication -- Preface -- Chapter 1: Classical Perspective -- 1.1 Importance of the Harmonic Oscillator -- 1.2 Newtonian Perspective -- 1.3 Restoring Force -- 1.4 Free Harmonic Oscillator -- 1.5 LC Resonator -- 1.6 Journey Through the Center of the Earth -- 1.7 Low Satellite Orbit -- 1.8 FREE-OSC, Free Oscillator Worksheet -- 1.9 Phase Space, Part 1 -- 1.10 PHASE-SP, Phase Space Worksheet -- 1.11 Callisto, Galileo, and French -- 1.12 Searching for Planets -- 1.13 Franklin, Priestly, Verne, and Burroughs -- What's Next? -- Chapter 2: Oscillator Energy -- 2.1 Conservative Forces -- 2.2 Potential Energy -- 2.3 Kinetic Energy -- 2.4 Conservation of Energy -- 2.5 Phase Space, Part 2 -- 2.6 Energy Diagrams -- 2.7 Equipartition of Energy -- 2.8 General Potential Energy Function -- 2.9 Perturbed Satellite Orbit -- 2.10 High Power-Law Oscillators -- 2.11 Adiabatic Invariance -- 2.12 UNDAMPED, Free Oscillator Energy Worksheet -- 2.13 Bungee Jumpers Beware -- 2.14 Summary -- Chapter 3: Damped Oscillators -- 3.1 Velocity-Dependent Resistive Force -- 3.2 FORCE-RV, Resistive Force Worksheet -- 3.3 Restoring Force and Resistive Force -- 3.4 Under-Damped Oscillator -- 3.5 Critically Damped Oscillator -- 3.6 Over-Damped Oscillator -- 3.7 Summary of Free, Damped Oscillators -- What's Next? -- Chapter 4: Forced Oscillators -- 4.1 Forced Free Mass -- 4.2 Forced Damped Mass -- 4.3 General Solution for Forced Damped Mass -- 4.4 Power Transfer -- 4.5 Forced Damped Oscillator -- 4.6 Permittivity for Bound Charges -- 4.7 FORCEOSC, Forced Oscillator Worksheet -- 4.8 Summary -- What's Next? -- Chapter 5: Q, R, X, Y, and Z -- 5.1 What Is Q? -- 5.2 Frequency Domain -- 5.3 Time Domain -- 5.4 Q of Various Oscillators -- 5.6 Resonant Detection, Mössbauer Effect -- 5.7 Q Multipliers and Dividers -- 5.8 Q Switches.

5.9 Classical Uncertainty Principle, Part 1 -- 5.10 ABC-OF-Q, Worksheet in Time and Frequency -- 5.11 Impedance and Admittance -- 5.12 Impedance and Admittance: Damped Mass -- 5.13 Impedance and Admittance: Harmonic Oscillator -- 5.14 Y-AND-Z, Admittance and Impedance Worksheet -- 5.15 How Henry Cavendish Weighed Planet Earth -- What's Next? -- Chapter 6: Fourier Perspective -- 6.1 Signal Classification -- 6.2 Periodic Signals -- 6.3 Oscillator with Periodic Force -- 6.4 Bandwidth and Spectral Density -- 6.5 Laplace's Equation -- 6.6 Non-Periodic Signals -- 6.7 Classical Uncertainty Principle, Part 2 -- 6.8 Alternative Formats -- 6.9 Laplace Transform -- 6.10 Hilbert Transform -- 6.11 Parseval's Theorem -- 6.12 Joint Time-Frequency Analysis -- 6.13 Inductive Leap -- What's Next? -- Chapter 7: Elements of Linear Systems -- 7.1 What Is a Linear System? -- 7.2 Ode to the Sinusoid -- 7.3 Fast Fourier Transform -- 7.4 Test Signals -- 7.5 Step Function Response -- 7.6 Impulse Response -- 7.7 Frequency Domain Response Using Phasors -- 7.8 Impulse Response and Causality -- 7.9 System Function via Fourier Transform -- 7.10 Impulse Response via Fourier Transform -- 7.11 Convolution -- 7.12 Power Spectral Density -- 7.13 Wiener-Khintchine Theorem -- 7.14 Auto- and Cross-Correlation Functions -- 7.15 Coherence Function -- 7.16 System Identification -- 7.17 Deconvolution -- 7.18 Data Windows -- 7.19 Central Limit Theorem -- What's Next? -- Chapter 8: Methods of Advanced Dynamics -- 8.1 Generalized Coordinates -- 8.2 Generalized Momenta -- 8.3 Lagrange's Equations -- 8.4 Hamilton's Equations -- 8.5 Poisson Brackets -- 8.6 Hamilton's Principle -- 8.7 Hamilton-Jacobi Equation -- 8.8 Symmetry of the Hamiltonian Function -- What's Next? -- Chapter 9: Coupled Oscillators -- 9.1 Two Coupled Oscillators -- 9.2 Magnetically Coupled Resonators.

9.3 COUPLOSC, Worksheet for Coupled Oscillators -- 9.4 Time Evolution, Weak Coupling -- 9.5 COUPLOS2, Worksheet #2 for Coupled Oscillators -- 9.6 Normal Coordinates -- 9.7 Oscillating Galaxies -- 9.8 Synchronized Oscillators -- What's Next? -- Chapter 10: Statistical Perspective -- 10.1 Distributions and Moments -- 10.2 Accuracy and Precision -- 10.3 Parable of the Bunny Rabbits -- 10.4 Displacement Probability Density -- 10.5 Uncertainty Due to Thermal Motion -- 10.6 More Distribution Functions -- 10.7 Natural Sources of Randomness -- 10.8 Poisson, Exponential, and Gaussian Distributions -- 10.9 Random Excitation -- 10.10 Entropy -- 10.11 Virial Theorem -- 10.12 Liouville's Theorem -- 10.13 Information and Noise -- 10.14 Stochastic Resonance -- 10.15 Phase Space Correlation and Covariance -- 10.16 Predictability -- 10.17 Time Evolution and Predictions -- 10.18 Expectation Values: Caveat Emptor -- 10.19 Expert Opinions on Predictability and Causality -- What's Next? -- Chapter 11: Quantum Perspective -- 11.1 Classical Crisis -- 11.2 A Collection of Oscillators -- 11.3 PLANCK, Worksheet for Blackbody Radiation -- 11.4 Harmonic Oscillators and Radiation -- 11.5 Wilson-Sommerfeld-Ishiwara Quantization Rule -- 11.6 Summary of Energy Level Spacing -- 11.7 Quantization of Angular Momentum -- What's Next? -- Chapter 12: Quantum Oscillators -- 12.1 Wave-Like Property of Momentum -- 12.2 Schrödinger Equation -- 12.3 Dynamic Variables and Their Operators -- 12.4 Free Particle -- 12.5 A Particle in a Box -- 12.6 Superposition of States -- 12.7 Electric Dipole Radiation -- 12.8 Dipole Transitions, Particle in a Box -- 12.10 Harmonic Oscillator -- 12.11 Harmonic Oscillator Dipole Transitions -- 12.12 QUANTOSC, Quantum Oscillator Worksheet -- 12.13 Revival of Wavefunctions -- 12.14 Discovery of Classical Oscillators -- 12.15 Meanwhile, Back in Heligoland ….

12.16 Single-Electron Oscillator -- 12.17 Trouble in Paradise -- What's Next? -- Appendix 1: Worksheets -- Installing the Files from the Diskette -- Useful Spreadsheet Functions -- Appendix 2: The Hilbert Transform -- A2.1 Derivation via Unit Step -- A2.2 Constructing an Analytic Function -- A2.3 Fourier Transform of Unit Step -- A2.4 Application of the Hilbert Transform -- A2.6 References for the Hilbert Transform -- Bibliography -- Books -- Software -- Selected Papers from American Journal of Physics -- Selected Papers from Other Journals -- Index.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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