a. Show that the density of states of a 2-D Fermi gas in a rectangular solid of dimension L2 equals N(E) = b. Show that the chemical potential of a Fermi gas in 2 dimensions is given by for n electrons per unit area. Use an integral table to solve the integral and watch your limits of integration. c. Show th ...continues
Consider a 2-level system with an energy splitting between the upper and lower level. Using Boltzmann statistics, show that the heat capacity of the 2-level system equals: (see attachment for equation) What happens in the limit of (see attachment for equation)
For a hydrogen atom in the ground state, calculate the probability of finding the electron in the "classically forbidden region."
Fermions in harmonic oscillator potential
Two identical, non-interacting spin-1/2 fermions are placed in the 1-D harmonic potential V(x) = (1/2)mω2x2, Where m is the mass of the fermion and ω is its angular frequency. a. Find the energies of the ground and first excited states of this two-fermion system. Express the eigenstates corresponding to the ...continues
I am having a hard time finding out how to work with the Raman effect using the Kramers-Heisenburg formula. I am calculating differential cross sections for scattering and I dont know how to do this or what approximations to use with the Raman effect. If anyone knows anything on this topic, please respond ASAP.
I am trying to do a problem considering the photoelectric effect with Hydrogen. I need to calculate the differential cross section for scattering taking into consideration a very high energy incident photon and high energy final electron. I do not know what kind of scattering this falls under. Rayleigh scattering is only for low ...continues
When an atom is placed in a uniform external electric field, the energy levels are shifted - a phenomenon known as the stark effect. In this problem we analyze the stark effect for the n=1 and n=2 states of hydrogen. See attached. Must be able to read microsoft word equation editor.
Calculate the angular spread of a laser beam due to diffraction if the beam emerges through a 2.90mm diameter mirror. Assume that lambda = 686nm.
1) For two distinguishable, non-interacting particles in a box, Quantum Mechanics says the energy must be ... (see attachment for remainder of problem)
Blackbody Radition in Flatland
Blackbody Radition in Flatland a) Carry out the derivation of u(v,t), the energy per unit area per unit frequency in the electromagnetic field, for the 2-dimentional case, i.e. inside a square cavity of side L held at temperature T. Find the total energy in the square and show that it's of the form: U(T) = (L^2)a(T^n) and det ...continues
