Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 Harmonic Oscillator
- 2 Damped Harmonic Oscillator
- 3 Coupled Oscillators
- 4 The Wave Equation
- 5 Integration
- 6 Waves in Three Dimensions
- 7 Other Wave Equations
- 8 Numerical Methods
- Appendix A Solving ODEs: A Roadmap
- Appendix B Vector Calculus: Curvilinear Coordinates
- References
- Index
7 - Other Wave Equations
Published online by Cambridge University Press: 02 April 2020
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 Harmonic Oscillator
- 2 Damped Harmonic Oscillator
- 3 Coupled Oscillators
- 4 The Wave Equation
- 5 Integration
- 6 Waves in Three Dimensions
- 7 Other Wave Equations
- 8 Numerical Methods
- Appendix A Solving ODEs: A Roadmap
- Appendix B Vector Calculus: Curvilinear Coordinates
- References
- Index
Summary
This chapter extends the discussion of waves beyond the longitudinal oscillations with which we began.Here, we look at the wave equation as it arises in electricity and magnetism, in Euler's equation and its shallow water approximation, in ``realistic" (extensible) strings, and in the quantum mechanical setting, culminating in a quantum mechanical treatment of the book's defining problem, the harmonic oscillator.
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- Mathematical Methods for Oscillations and Waves , pp. 181 - 206Publisher: Cambridge University PressPrint publication year: 2020