Book contents
- Frontmatter
- Contents
- Preface to Part 1
- Preface to Part 2
- Preface to the combined volume
- 1 General introduction – author to reader
- PART 1 THE SIMPLE CLASSICAL VIBRATOR
- PART 2 THE SIMPLE VIBRATOR IN QUANTUM MECHANICS
- 13 The quantized harmonic vibrator and its classical features
- 14 Anharmonic vibrators
- 15 Vibrations and cyclotron orbits in two dimensions
- 16 Dissipation, level broadening and radiation
- 17 The equivalent classical oscillator
- 18 The two-level system
- 19 Line broadening
- 20 The ammonia maser
- 21 The family of masers: from laser to travelling-wave oscillator
- Epilogue
- References
- Index
13 - The quantized harmonic vibrator and its classical features
Published online by Cambridge University Press: 13 January 2010
- Frontmatter
- Contents
- Preface to Part 1
- Preface to Part 2
- Preface to the combined volume
- 1 General introduction – author to reader
- PART 1 THE SIMPLE CLASSICAL VIBRATOR
- PART 2 THE SIMPLE VIBRATOR IN QUANTUM MECHANICS
- 13 The quantized harmonic vibrator and its classical features
- 14 Anharmonic vibrators
- 15 Vibrations and cyclotron orbits in two dimensions
- 16 Dissipation, level broadening and radiation
- 17 The equivalent classical oscillator
- 18 The two-level system
- 19 Line broadening
- 20 The ammonia maser
- 21 The family of masers: from laser to travelling-wave oscillator
- Epilogue
- References
- Index
Summary
By the time a student of physics is ready to tackle quantum mechanics he has become familiar with the classical harmonic vibrator through many examples, and knows the crucial role it played in the development of Planck's ideas. It is natural then to concentrate on the mathematical aspects of the harmonic oscillator equation in quantum mechanics, the solution of Schrödinger's equation, normalization of the wave-function, calculation of mean values and of matrix elements, leaving the physics to look after itself. At a more advanced level the harmonic vibrator provides the entry into field theories, second quantization etc., and as a general rule it tends to be viewed more as a vehicle for instruction in more interesting matters than as a physical system having its own considerable interest and importance. Here we shall seek to redress the balance and study the vibrator as a thing in itself, without losing sight of the variety of physical problems to which the results can be applied. One especially important set of applications, however, will get little attention at this stage – the vibrations of compound bodies and of extended physical systems provide such wealth of interest as to justify a volume to themselves; and it is to such matters that the whole of the third part of this work will be devoted. As soon as one begins to contemplate the harmonic vibrator one becomes aware of the exceptional nature of its behaviour, in that it conforms more closely than any other system to the classical rules.
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- Information
- The Physics of Vibration , pp. 427 - 451Publisher: Cambridge University PressPrint publication year: 1989