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- Consider a particle of mass moving in a three-dimensional
isotropic harmonic oscillator potential of force constant . Solve the
problem via the separation of variables, and obtain an expression for
the allowed values of the total energy of the system (in a stationary state).
- Repeat the calculation of the Fermi energy of a gas of fermions by
assuming that the fermions are massless, so that the energy-momentum relation
is .
- Calculate the density of states of an electron gas in a cubic
box of volume , bearing in mind that there are two electrons
per energy state. In other words, calculate the number of electron
states in the interval to . This number can be written
,
where is the density of states.
- Repeat the above calculation for a two-dimensional electron
gas in a square box of area .
- Given that the number density of free electrons in copper is
, calculate the Fermi
energy in electron volts, and the velocity of an electron whose kinetic
energy is equal to the Fermi energy.
- Obtain an expression for the Fermi energy (in eV) of an electron in a white
dwarf star as a function of the stellar mass (in solar masses). At what
mass does the Fermi energy equal the rest mass energy?

** Next:** Orbital Angular Momentum
** Up:** White-Dwarf Stars
** Previous:** White-Dwarf Stars
Richard Fitzpatrick
2010-07-20