2лх Consider a one dimensional lattice with a weak periodic potential U (x) =U, cos a The gap at the edge of the Brillouin zone | k is: %3D a (a) U, U. (b) (c) 2U, (d)
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- (a) Write the expression of average no. of particle (s) in particular single particle quantum state (s) for a quantum gas of N identical particle at temp. T. If partilcle is fermion then show that- Here B - ns = 1 kT 1 ea+Bei +1 energy of state.Plz don't use chat gptA hypothetical laser operating at 632 nm has a output of powe 1.0mW witha 1 mm beam diameter. If the energy density for this system is u(v) = 5.33× 10-12 J – s/m³ fine the following (a) The ratio of stimulated emmission to spontaneous radiation. (b) The effective blackbody temperature of the system. %3D
- Asap plz3For 3D free electron gas, the density of states counts the number of degenerate electron states dn per energy interval dE around a given energy E as g(E): = dn dE 3 (2m₂)2V 1 E2 2π²ħ³ At absolute zero temperature, N electrons can fill up all low lying energy levels (following Pauli exclusion principle) up to a given energy level E called Fermi energy. From the density of states, what is the relation between the total electron states N below a given energy E? Use this result to show that the Fermi energy EF is given by - - 2010 (307² M)³ ħ² 3π²N\3 EF 2me V
- An arbitrary quantm mechanical system is initially in the ground state |0). At t = 0, a perturbation of the form H' (t) = Hoc:/T is applied. Show that at large times the probability that. tlhe system is in state |1) is given by |(0}Ho|1}|2 (A) A + (Ac)? where As is the difference in cnergy of states |0) and |1). Be specific about what assumption, if any, were inade arriving at your conclusion.explain the Fermi Dirac distributionThe atoms of an FCC lattice are hard spheres touching the surfaces of the nearest neighbors. f the effective radius of atom is 4.25 Angstrom, what is the volume density (cm 3)?