Transcription of Density of States - United States Naval Academy
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Density of States - United States Naval Academy
Density of States Mungan, Spring 2000 According to Stowe Eq. ( ), the Density of States g(E) is given by g(E)!En/2 (1) where E is the internal energy of a system and n is its number of degrees of freedom. For a single particle in a 3D box, n = 3 due to the three independent translational kinetic energy terms, E=px22m+py22m+pz22m!p22m. (2) Thus, according to Eq. (1), we would expect the Density of States to vary with the energy to the 3/2 power. In fact, however, quantum mechanics gives a different answer. According to the de Broglie relation and the boundary condition that there must be nodes in the wavefunction (of wavelength ) at the walls of the cubical box (of length L on a side), we have px=h!
Clearly Stowe’s derivation in this Appendix needs patching up. The number of states accessible to the ith degree of freedom is proportional to the “volume” ... If the density of states is linearly proportional to energy, then Eq. (10) implies that n = 4, not n = 2 from Eq. (1).
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ECE3080-L-4-Density of states, Derivation, Density of states, Of states, 1. Boltzmann distribution, Boltzmann distribution, The density of electronic states in, States, Density, Density Matrix, Intrinsic Carrier Concentration, Density states, Quantum Theory of Thermoelectric Power Seebeck, Intrinsiccarrierconcentrationinsemiconductors, Density of States, Fermi Energy and Energy, Handout 7. Entropy