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Introduction to Classic and Quantum Harmonic Oscillators [Multiple-component retail product]

  • Formāts: Multiple-component retail product, 368 pages, height x width: 195x240 mm, weight: 907 g, Illustrations, Contains 1 Hardback and 2 diskettes
  • Izdošanas datums: 18-Feb-1997
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 0471147443
  • ISBN-13: 9780471147442
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Introduction to Classic and Quantum Harmonic OscillatorsPalielināt
  • Formāts: Multiple-component retail product, 368 pages, height x width: 195x240 mm, weight: 907 g, Illustrations, Contains 1 Hardback and 2 diskettes
  • Izdošanas datums: 18-Feb-1997
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 0471147443
  • ISBN-13: 9780471147442
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780471147442.html
Keywords:
Harmonic oscillation is a key to understanding the physical universe and a linchpin in a diversity of fields, including mechanics, electromagnetics, electronics, optics, acoustics, and quantum mechanics. This introduction to how harmonic oscillators function and the analytical systems used to describe them is for professionals and students in electrical engineering, mechanical engineering, physics, and chemistry. The included disk allows use of spreadsheets (in Microsoft Excel, Quattro Pro, or Lotus 1-2-3) for graphic display of complex relationships without painstaking calculation. Annotation c. by Book News, Inc., Portland, Or.

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.
Preface xv
Chapter 1 Classical Perspective
1(24)
1.1 Importance of the Harmonic Oscillator
1(3)
Degrees of freedom
2(1)
Need for a statistical description
3(1)
1.2 Newtonian Perspective
4(2)
Inertial Coordinate System
5(1)
1.3 Restoring Force
6(3)
1.4 Free Harmonic Oscillator
9(4)
Magnitude and Phase
12(1)
Phasor solution
12(1)
1.5 LC Resonator
13(1)
1.6 Journey Through the Center of the Earth
14(3)
1.7 Low Satellite Orbit
17(1)
1.8 FREE-OSC, Free Oscillator Worksheet
18(1)
1.9 Phase Space, Part 1
19(2)
1.10 PHASE-SP, Phase Space Worksheet
21(1)
1.11 Callisto, Galileo, and French
22(1)
1.12 Searching for Planets
22(1)
1.13 Franklin, Priestly, Verne, and Burroughs
23(1)
What's Next?
24(1)
Chapter 2 Oscillator Energy
25(20)
2.1 Conservative Forces
25(1)
Force Test
26(1)
2.2 Potential Energy
26(2)
2.3 Kinetic Energy
28(1)
2.4 Conservation of Energy
29(1)
2.5 Phase Space, Part 2
29(2)
2.6 Energy Diagrams
31(3)
2.7 Equipartition of Energy
34(1)
2.8 General Potential Energy Function
34(2)
2.9 Perturbed Satellite Orbit
36(3)
2.10 High Power-Law Oscillators
39(2)
A Particle in a Box
39(2)
2.11 Adiabatic Invariance
41(1)
2.12 UNDAMPED, Free Oscillator Energy Worksheet
42(1)
2.13 Bungee Jumpers Beware
43(1)
2.14 Summary
44(1)
Chapter 3 Damped Oscillators
45(20)
3.1 Velocity-Dependent Resistive Force
45(3)
Time Constant and Half-Life
47(1)
3.2 FORCE-RV, Resistive Force Worksheet
48(1)
3.3 Restoring Force and Resistive Force
49(1)
3.4 Under-Damped Oscillator
50(5)
UNDRDAMP, Under-Damped Worksheet
53(1)
Energy and Power Loss
53(2)
3.5 Critically Damped Oscillator
55(3)
CRITDAMP, Critically Damped Worksheet
56(2)
3.6 Over-Damped Oscillator
58(3)
OVERDAMP, Over-Damped Worksheet
59(2)
3.7 Summary of Free, Damped Oscillators
61(3)
Transition from Under-Damped Oscillation
62(1)
Transition from Over-Damped Oscillation
62(2)
What's Next?
64(1)
Chapter 4 Forced Oscillators
65(28)
4.1 Forced Free Mass
65(7)
FREEMASS, Worksheet for a Forced Free Mass
69(1)
Permittivity and Index of Refraction, Free Charges
69(3)
4.2 Forced Damped Mass
72(4)
Time Domain
72(1)
Frequency Domain (Phasor Solution)
73(1)
Permittivity and Index of Refraction, Damped Free Charges
74(2)
4.3 General Solution for Forced Damped Mass
76(4)
Impulse or Delta Function Response
77(1)
Random Impulse Response
78(1)
Step Function Response
78(1)
Sinusoidal Response
79(1)
4.4 Power Transfer
80(1)
DAMPMASS, Worksheet for Forced, Damped Mass
80(1)
4.5 Forced Damped Oscillator
80(8)
Displacement
81(2)
Displacement Resonance
83(1)
Velocity
84(1)
Velocity Resonance
85(1)
Power Resonance
86(1)
Energy Resonance
86(2)
4.6 Permittivity for Bound Charges
88(2)
Lorentz Line Shape
88(2)
4.7 FORCEOSC, Forced Oscillator Worksheet
90(1)
4.8 Summary
90(1)
What's Next?
91(2)
Chapter 5 Q, R, X, Y, and Z
93(26)
5.1 What Is Q?
93(2)
5.2 Frequency Domain
95(5)
Rate of Change of Phase
96(3)
Loss Tangent and Dissipation Factor
99(1)
5.3 Time Domain
100(2)
5.4 Q of Various Oscillators
102(1)
5.6 Resonant Detection, Mossbauer Effect
103(1)
5.7 Q Multipliers and Dividers
104(1)
5.8 Q Switches
105(1)
5.9 Classical Uncertainty Principle, Part 1
105(1)
5.10 ABC-OF-Q, Worksheet in Time and Frequency
106(1)
5.11 Impedance and Admittance
107(1)
5.12 Impedance and Admittance: Damped Mass
108(2)
5.13 Impedance and Admittance: Harmonic Oscillator
110(4)
5.14 Y-AND-Z, Admittance and Impedance Worksheet
114(1)
5.15 How Henry Cavendish Weighed Planet Earth
114(3)
What's Next?
117(2)
Chapter 6 Fourier Perspective
119(40)
6.1 Signal Classification
120(1)
6.2 Periodic Signals
120(6)
Fourier Series
121(1)
Restrictions on Fourier Series
122(1)
Square Wave
122(2)
Triangular Wave
124(1)
FOURIER, Fourier Series Worksheet
125(1)
6.3 Oscillator with Periodic Force
126(1)
6.4 Bandwidth and Spectral Density
127(3)
6.5 Laplace's Equation
130(4)
Cauchy-Riemann Equations
131(3)
6.6 Non-Periodic Signals
134(10)
Fourier Transform
134(1)
Centered Rectangular Pulse
134(3)
Pulse Bandwidth
137(1)
Uncentered Rectangular Pulse
137(3)
Exponential Decay
140(1)
Oscillatory Exponential Decay
141(3)
6.7 Classical Uncertainty Principle, Part 2
144(4)
Rectangular Pulse
145(1)
Non-Oscillatory Exponential Decay
145(1)
Oscillatory Exponential Decay
145(1)
Gaussian Function
145(3)
6.8 Alternative Formats
148(2)
Discrete Fourier Transform
150(1)
6.9 Laplace Transform
150(2)
6.10 Hilbert Transform
152(2)
6.11 Parseval's Theorem
154(1)
6.12 Joint Time-Frequency Analysis
154(1)
6.13 Inductive Leap
155(1)
What's Next?
156(3)
Chapter 7 Elements of Linear Systems
159(38)
7.1 What Is a Linear System?
159(1)
7.2 Ode to the Sinusoid
160(1)
7.3 Fast Fourier Transform
161(4)
7.4 Test Signals
165(1)
7.5 Step Function Response
165(1)
7.6 Impulse Response
166(1)
7.7 Frequency Domain Response Using Phasors
166(4)
7.8 Impulse Response and Causality
170(1)
Causality and the Hilbert Transform
170(1)
7.9 System Function via Fourier Transform
171(1)
7.10 Impulse Response via Fourier Transform
171(1)
7.11 Convolution
172(5)
Convolution Theorem
174(1)
CONVOLVE, Convolution Worksheet
175(2)
7.12 Power Spectral Density
177(1)
7.13 Wiener-Khintchine Theorem
178(1)
7.14 Auto- and Cross-Correlation Functions
178(4)
Correlation Function without FFT
178(1)
Applications of Auto- and Cross-Correlation
179(1)
CROSSCOR, Cross-Correlation Worksheet
180(2)
7.15 Coherence Function
182(2)
7.16 System Identification
184(3)
7.17 Deconvolution
187(3)
7.18 Data Windows
190(3)
7.19 Central Limit Theorem
193(3)
What's Next?
196(1)
Chapter 8 Methods of Advanced Dynamics
197(14)
8.1 Generalized Coordinates
197(2)
Coordinate Transformation
198(1)
8.2 Generalized Momenta
199(1)
8.3 Lagrange's Equations
200(2)
Harmonic Oscillator
201(1)
8.4 Hamilton's Equations
202(2)
Harmonic Oscillator
203(1)
8.5 Poisson Brackets
204(1)
8.6 Hamilton's Principle
205(2)
8.7 Hamilton-Jacobi Equation
207(2)
8.8 Symmetry of the Hamiltonian Function
209(1)
What's Next?
210(1)
Chapter 9 Coupled Oscillators
211(14)
9.1 Two Coupled Oscillators
212(2)
Normal Mode Frequencies
213(1)
9.2 Magnetically Coupled Resonators
214(1)
9.3 COUPLOSC, Worksheet for Coupled Oscillators
215(1)
9.4 Time Evolution, Weak Coupling
216(3)
9.5 COUPLOS2, Worksheet #2 for Coupled Oscillators
219(1)
9.6 Normal Coordinates
219(3)
9.7 Oscillating Galaxies
222(1)
9.8 Synchronized Oscillators
222(2)
Synchronize Your PC to an Atomic Clock
224(1)
What's Next?
224(1)
Chapter 10 Statistical Perspective
225(36)
10.1 Distributions and Moments
225(4)
Moments to Remember
226(3)
10.2 Accuracy and Precision
229(1)
10.3 Parable of the Bunny Rabbits
230(1)
Ensemble preparation
230(1)
Measurements
230(1)
10.4 Displacement Probability Density
231(4)
PROBABIL, Classical Oscillator Probability Worksheet
235(1)
10.5 Uncertainty Due to Thermal Motion
235(3)
Uncertainty Principle, Part 3
237(1)
10.6 More Distribution Functions
238(1)
10.7 Natural Sources of Randomness
239(2)
10.8 Poisson, Exponential, and Gaussian Distributions
241(3)
Poisson Distribution
242(1)
Exponential Distribution
242(1)
Gaussian (Normal) Distribution
243(1)
10.9 Random Excitation
244(2)
10.10 Entropy
246(2)
10.11 Virial Theorem
248(2)
10.12 Liouville's Theorem
250(1)
10.13 Information and Noise
250(1)
10.14 Stochastic Resonance
251(1)
10.15 Phase Space Correlation and Covariance
252(2)
10.16 Predictability
254(3)
10.17 Time Evolution and Predictions
257(1)
10.18 Expectation Values: Caveat Emptor
258(1)
10.19 Expert Opinions on Predictability and Causality
259(1)
What's Next?
260(1)
Chapter 11 Quantum Perspective
261(18)
11.1 Classical Crisis
261(4)
Blackbody Radiation
262(3)
11.2 A Collection of Oscillators
265(4)
Planck Distribution
266(3)
11.3 PLANCK, Worksheet for Blackbody Radiation
269(1)
11.4 Harmonic Oscillators and Radiation
270(2)
11.5 Wilson-Sommerfeld-Ishiwara Quantization Rule
272(3)
Simple Harmonic Oscillator
272(1)
A Particle in a One-Dimensional Box
273(2)
11.6 Summary of Energy Level Spacing
275(1)
11.7 Quantization of Angular Momentum
276(2)
What's Next?
278(1)
Chapter 12 Quantum Oscillators
279(42)
12.1 Wave-Like Property of Matter
279(3)
12.2 Schrodinger Equation
282(2)
12.3 Dynamic Variables and Their Operators
284(2)
12.4 Free Particle
286(5)
Group, Phase, and Classical Velocities
287(4)
12.5 A Particle in a Box
291(5)
Separation of Variables
291(4)
Probability of Finding the Particle
295(1)
12.6 Superposition of States
296(3)
Schrodinger's Cat and Her Kitten
298(1)
Wave Packet Spreading
298(1)
12.7 Electric Dipole Radiation
299(1)
12.8 Dipole Transitions, Particle in a Box
300(1)
12.10 Harmonic Oscillator
301(6)
Zero-Point Energy
302(1)
Harmonic Oscillator Wavefunctions
302(3)
Ground state, n = 0
305(1)
First excited state, n = 1
306(1)
Second excited state, n = 2
307(1)
Tenth excited state, n = 10
307(1)
12.11 Harmonic Oscillator Dipole Transitions
307(1)
12.12 QUANTOSC, Quantum Oscillator Worksheet
308(1)
12.13 Revival of Wavefunctions
309(1)
12.14 Discovery of Classical Oscillators
309(2)
12.15 Meanwhile, Back in Heligoland...
311(3)
Quantum Extension of Classical Formalism
311(1)
Harmonic Oscillator
312(2)
12.16 Single-Electron Oscillator
314(1)
12.17 Trouble in Paradise
315(1)
What's Next?
316(5)
Statistical Interpretation
317(1)
Expansion of the Universe
317(1)
Superstrings
317(4)
Appendix 1 Worksheets 321(4)
Installing the Files from the Diskettes 321(1)
Useful Spreadsheet Functions 322(3)
Appendix 2 The Hilbert Transform 325(8)
A2.1 Derivation via Unit Step 326(1)
A2.2 Constructing an Analytic Function 327(1)
A2.3 Fourier Transform of Unit Step 327(2)
A2.4 Application of the Hilbert Transform 329(2)
Hilbert and Vitamin B12 331(1)
A2.6 References for the Hilbert Transform 331(2)
Bibliography 333(26)
Books 333(1)
Software 334(1)
Selected Papers from American Journal of Physics 335(13)
Selected Papers from Other Journals 348(11)
Index 359
S. C. BLOCH is a professor at the University of South Florida. His research areas include satellite communications and electromagnetic properties of plasmas.