  In our previous paper, we have investigated the thermodynamics of the quantum
ultra-cold neutron gas trapped in the two-dimensional square-well potential on
the Earth's gravitational field. We have pointed out that they have strong
dependence on the shape of the trapping potential. In the present paper, we
estimate the Fermi energy and the density distribution of the Fermi gas with
two-dimensional harmonic oscillator potential, instead of the square-well
potential. Then we discuss them in terms of the Fermi energy and the density
distribution as compared with both of cases.
