Homework 6

Problem 1:

A one-dimensional periodic potential consists of a sequence of Dirac delta functions with a distance d between them.  (This is called the Dirac comb.)

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Determine the energy eigenvalues of this potential.

Problem 2:

Consider a Fermi gas model of the nucleus consisting of independent proton and neutron Fermi gases.  Derive expressions for the Fermi energies of both the proton and the neutron gases consisting of N neutrons and Z protons respectively, where N+Z=A, the mass number of the nucleus.  If the radius of a nucleus is given by R=1.2A1/3fm and mp»mn=1.6´10-24g, calculate the numerical values of the Fermi energies for 198Au.