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
16 - Dissipation, level broadening and radiation
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
After this excursion into the field of non-linear vibrators, we now return to the harmonic vibrator and take up a point which had begun to reveal itself at the end of chapter 13, where we found that under the influence of a uniform, but arbitrarily time-varying, force the vibrator never forgets its initial state. If it started in the ground state, for ever afterwards its response can be described by the movement of a compact distribution in the σ-representation of equivalent classical vibrators; only the centroid of the distribution responds to the applied force. The harmonic vibrator is thus extraordinarily resistant to randomization. To be sure, if the force is not uniform, but depends on the displacement of the oscillating particle, the result just summarized is no longer true. Nevertheless, in the most important application, where an oscillator of atomic dimensions is influenced by electromagnetic vibrations, the force due to the electric field is as nearly uniform as makes no difference, since the wavelength of electromagnetic waves at a typical atomic resonant frequency is a thousand times the size of an atom. The disturbing aspect of the resistance of a vibrator to randomization is that in all theories of black-body radiation, before and after Planck, it is assumed that material oscillators and electromagnetic vibrations in a cavity will eventually share the chaotic state that allows statistical mechanics to be applied.
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- Chapter
- Information
- The Physics of Vibration , pp. 489 - 509Publisher: Cambridge University PressPrint publication year: 1989