Abstract
The density of states is a rather important property not only for photons but for any (quasi-)particle. Thus we will discuss this quantity in a rather general way which can then also be used throughout this book for the statistics of any type of (quasi-)particles including systems of reduced dimensionality. To describe the probability that the available states are occupied with (quasi-)particles we will introduce respective distribution functions for fermionic and bosonic particles.
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References
H. Ibach, H. Lüth, Solid-State Physics, 4th edn. (Springer, Berlin, 2009)
S. Hunklinger, Festkörperphysik, 4th edn. (De Gruyter Oldenbourg, Oldenbourg, 2014)
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Problems
4.1
Check whether the maximum of \(N(\omega )\) in (4.23) shifts in proportion to T (Wien’s law), originally formulated as \(\lambda _{{\text {max}}}\propto T^{-1}\).
4.2
How does the density of states as a function of energy vary for a linear dispersion relation (like photons) in 3, 2 and 1 dimensional systems?
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Kalt, H., Klingshirn, C.F. (2019). Density of States and Distribution Functions. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_4
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DOI: https://doi.org/10.1007/978-3-030-24152-0_4
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Online ISBN: 978-3-030-24152-0
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