Book contents
- Frontmatter
- Contents
- Preface
- 1 Central concepts in classical mechanics
- 2 Central concepts in classical electromagnetism
- 3 Central concepts in quantum mechanics
- 4 Central concepts in stationary quantum theory
- 5 Central concepts in measurement theory
- 6 Wigner's phase-space representation
- 7 Hamiltonian formulation of classical electrodynamics
- 8 System Hamiltonian of classical electrodynamics
- 9 System Hamiltonian in the generalized Coulomb gauge
- 10 Quantization of light and matter
- 11 Quasiparticles in semiconductors
- 12 Band structure of solids
- 13 Interactions in semiconductors
- 14 Generic quantum dynamics
- 15 Cluster-expansion representation of the quantum dynamics
- 16 Simple many-body systems
- 17 Hierarchy problem for dipole systems
- 18 Two-level approximation for optical transitions
- 19 Self-consistent extension of the two-level approach
- 20 Dissipative extension of the two-level approach
- 21 Quantum-optical extension of the two-level approach
- 22 Quantum dynamics of two-level system
- 23 Spectroscopy and quantum-optical correlations
- 24 General aspects of semiconductor optics
- 25 Introductory semiconductor optics
- 26 Maxwell-semiconductor Bloch equations
- 27 Coherent vs. incoherent excitons
- 28 Semiconductor luminescence equations
- 29 Many-body aspects of excitonic luminescence
- 30 Advanced semiconductor quantum optics
- Appendix Conservation laws for the transfer matrix
- Index
- References
3 - Central concepts in quantum mechanics
Published online by Cambridge University Press: 05 January 2012
- Frontmatter
- Contents
- Preface
- 1 Central concepts in classical mechanics
- 2 Central concepts in classical electromagnetism
- 3 Central concepts in quantum mechanics
- 4 Central concepts in stationary quantum theory
- 5 Central concepts in measurement theory
- 6 Wigner's phase-space representation
- 7 Hamiltonian formulation of classical electrodynamics
- 8 System Hamiltonian of classical electrodynamics
- 9 System Hamiltonian in the generalized Coulomb gauge
- 10 Quantization of light and matter
- 11 Quasiparticles in semiconductors
- 12 Band structure of solids
- 13 Interactions in semiconductors
- 14 Generic quantum dynamics
- 15 Cluster-expansion representation of the quantum dynamics
- 16 Simple many-body systems
- 17 Hierarchy problem for dipole systems
- 18 Two-level approximation for optical transitions
- 19 Self-consistent extension of the two-level approach
- 20 Dissipative extension of the two-level approach
- 21 Quantum-optical extension of the two-level approach
- 22 Quantum dynamics of two-level system
- 23 Spectroscopy and quantum-optical correlations
- 24 General aspects of semiconductor optics
- 25 Introductory semiconductor optics
- 26 Maxwell-semiconductor Bloch equations
- 27 Coherent vs. incoherent excitons
- 28 Semiconductor luminescence equations
- 29 Many-body aspects of excitonic luminescence
- 30 Advanced semiconductor quantum optics
- Appendix Conservation laws for the transfer matrix
- Index
- References
Summary
In the early 1900s more and more experimental evidence was accumulated indicating that microscopic particles show wave-like properties in certain situations. These particle-wave features are very evident, e.g., in measurements where electrons are diffracted from a double slit to propagate toward a screen where they are detected. Based on the classical averaging of particles discussed in Section 1.2.2, one expects that the double slit only modulates the overall intensity, not the spatial distribution. Experimentally, however, one observes a nearly perfect interference pattern at the screen implying that the electrons exhibit wave averaging features such as discussed in Section 2.1.2. This behavior, originally unexpected for particle beams, persists even if the experiment is repeated such that only one electron at a time passes the double slit before it propagates to the detection screen. Thus, the wave aspect must be an inherent property of individual electrons and not an ensemble effect.
Another, independent argument for the failure of classical physics is that the electromagnetic analysis of atoms leads to the conclusion that the negatively charged electron(s) should collapse into the positively charged ion because the electron–ion system loses its energy due to the emission of radiation. As we will see, this problem can be solved by including the wave aspects of particles into the analysis. In particular, as discussed in Section 2.3.3, waves can never be localized to a point without increasing their momentum and energy beyond bounds.
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- Information
- Semiconductor Quantum Optics , pp. 48 - 64Publisher: Cambridge University PressPrint publication year: 2011