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- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/09%3A_Condensed_Matter_Physics/9.05%3A_Free_Electron_Model_of_MetalsMetals conduct electricity, and electricity is composed of large numbers of randomly colliding and approximately free electrons. The allowed energy states of an electron are quantized. This quantizati...Metals conduct electricity, and electricity is composed of large numbers of randomly colliding and approximately free electrons. The allowed energy states of an electron are quantized. This quantization appears in the form of very large electron energies, even at T=0 K. The allowed energies of free electrons in a metal depend on electron mass and on the electron number density of the metal.
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Thermodynamics_and_Statistical_Mechanics_(Arovas)/04%3A_Statistical_Ensembles/4.01%3A_Microcanonical_Ensemble_(CE)Note that D(E) has dimensions of inverse energy, so one might ask how we are to take the logarithm of a dimensionful quantity in Equation ???. We must introduce an energy scale, such as ...Note that D(E) has dimensions of inverse energy, so one might ask how we are to take the logarithm of a dimensionful quantity in Equation ???. We must introduce an energy scale, such as \RDeltaE in Equation ???, and define ˜D(E;\RDeltaE)=D(E)\RDeltaE and S(E;\RDeltaE)≡\kBln˜D(E;\RDeltaE).
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/02%3A_Resonances/2.04%3A_Fermi's_Golden_RuleWe can determine f(t) by first studying its Fourier transform, \[F(\omega) \;=\; \int_{-\infty}^\infty dt \; e^{i\omega t}\, f(t) \;=\; \int_0^\infty dt \; e^{i(\omega + i\varepsilon) t} \; \langl...We can determine f(t) by first studying its Fourier transform, F(ω)=∫∞−∞dteiωtf(t)=∫∞0dtei(ω+iε)t⟨φ|e−iˆHt/ℏ|φ⟩. Now insert a resolution of the identity, ˆI=∑n|n⟩⟨n|, where {|n⟩} denotes the exact eigenstates of ˆH (for free states, the sum goes to an integral in the usual way): \[\begin{align} \begin{aligned}F(\…
