Waves and Oscillations A Prelude to Quantum Mechanics

ISBN-10: 019539349X
ISBN-13: 9780195393491
Edition: 2010
Authors: Walter Fox Smith
List price: $79.00 Buy it from $25.61
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Description: Waves and oscillations permeate virtually every field of current physics research, are central to chemistry, and are essential to much of engineering. Furthermore, the concepts and mathematical techniques used for serious study of waves and  More...

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Book details

List price: $79.00
Copyright year: 2010
Publisher: Oxford University Press, Incorporated
Publication date: 5/20/2010
Binding: Hardcover
Pages: 400
Size: 7.25" wide x 10.00" long x 1.00" tall
Weight: 2.244
Language: English

Waves and oscillations permeate virtually every field of current physics research, are central to chemistry, and are essential to much of engineering. Furthermore, the concepts and mathematical techniques used for serious study of waves and oscillations form the foundation for quantum mechanics. Once they have mastered these ideas in a classical context, students will be ready to focus on the challenging concepts of quantum mechanics when they encounter them, rather than struggling with techniques. This lively textbook gives a thorough grounding in complex exponentials and the key aspects of differential equations and matrix math; no prior experience is assumed. The parallels between normal mode analysis, orthogonal function analysis (especially Fourier analysis), and superpositions of quantum states are clearly drawn, without actually getting into the quantum mechanics. An in-depth, accessible introduction to Hilbert space and bra-ket notation begins in Chapter 5 (on symmetrical coupled oscillators), emphasizing the analogy with conventional dot products, and continues in subsequent chapters. Connections to current physics research (atomic force microscopy, chaos, supersolids, micro electro-mechanical systems (MEMS), magnetic resonance imaging, carbon nanotubes, and more) are highlighted in the text and in end-of-chapter problems, and are frequently updated in the associated website. The book actively engages readers with a refreshing writing style and a set of carefully applied learning tools, such as in-text concept tests, "your turn" boxes (in which the student fills in one or two steps of a derivation), concept and skill inventories for each chapter, and "wrong way" problems in which the student explains the flaw in a line of reasoning. These tools promote self-awareness of the learning process. The associated website features custom-developed applets, video and audio recordings, additional problems, and links to related current research. The instructor-only part includes difficulty ratings for problems, optional hints, full solutions, and additional support materials.

Learning Tools Used in This Book
Simple Harmonic Motion
Sinusoidal oscillations are everywhere
The physics and mathematics behind simple sinusoidal motion
Important parameters and adjustable constants of simple harmonic motion
Mass on a spring
Electrical oscillators
Review of Taylor series approximations
Euler's equation
Review of complex numbers
Complex exponential notation for oscillatory motion
The complex representation for AC circuits
Another important complex function: The quantum mechanical wavefunction
Pure sinusoidal oscillations and uncertainty principles
Concept and skill inventory
Problems
Examples of Simple Harmonic Motion
Requirements for harmonic oscillation
Pendulums
Elastic deformations and Young's modulus
Shear
Torsion and torsional oscillators
Bending and Cantilevers
Concept and skill inventory
Problems
Damped Oscillations
Damped mechanical oscillators
Damped electrical oscillators
Exponential decay of energy
The quality factor
Underdamped, overdamped, and critically damped behavior
Types of damping
Concept and skill inventory
Problems
Driven Oscillations and Resonance
Resonance
Effects of damping
Energy flow
Linear differential equations the superposition principle for driven systems, and the response to multiple drive forces
Transients
Electrical resonance
Other examples of resonance: MRT and other spectroscopies
Nonlinear oscillators and chaos
Concept and skill inventory
Problems
Symmetric Coupled Oscillators and Hilbert Space
Beats: An aside?
Two symmetric coupled oscillators: Equations of motion
Normal modes
Superposing normal modes
Normal mode analysis, and normal modes as an alternate description of reality
Hilbert space and bra-ket notation
The analogy between coupled oscillators and molecular energy levels
Nonzero initial velocities
Damped, driven coupled oscillators
Concept and skill inventory
Problems
Asymmetric Coupled Oscillators and the Eigenvalue Equation
Matrix math
Equations of motion and the eigenvalue equation
Procedure for solving the eigenvalue equation
Systems with more than two objects
Normal mode analysis for multi-object, asymmetrical systems
More matrix math
Orthogonality of normal modes, normal mode coordinates, degeneracy, and scaling of Hilbert space for unequal masses
Concept and skill inventory
Problems
String Theory
The beaded string
Standing wave guess: Boundary conditions quantize the allowed frequencies
The highest possible frequency; connection to waves in a crystalline solid
Normal mode analysis for the beaded string
Longitudinal oscillations
The continuous string
Normal mode analysis for continuous systems
k-space
Concept and skill inventor
Problems
Fourier Analysis
Introduction
The Fourier Expansion
Expansions using nonnormalized orthogonal basis functions
Finding the coefficients in the Fourier series expansion
Fourier Transforms and the meaning of negative frequency
The Discrete Fourier Transform (DFT)
Some applications of Fourier Analysis
Concept and skill inventory
Problems
Traveling Waves
Introduction
The wave equation
Traveling sinusoidal waves
The superposition principle for traveling waves
Electromagnetic waves in vacuum
Electromagnetic waves in matter
Waves on transmission lines
Sound waves
Musical instruments based on tubes
Power carried by rope and electromagnetic waves; RMS amplitudes
Intensity of sound waves; decibels
Dispersion relations and group velocity
Concept and skill inventory
Problems
Waves at Interfaces
Reflections and the idea of boundary conditions
Transmitted waves
Characteristic impedances for mechanical systems
�Universal� expressions for transmission and reflection
Reflected and transmitted waves for transmission lines
Reflection and transmission for electromagnetic waves in matter: Normal incidence
Reflection and transmission for sound waves, and summary of isomorphisms
Snell's Law
Total internal reflection and evanescent waves
Concept and skill inventory
Problems
Group Velocity for an Arbitrary Envelope Function
Index

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