| Summary: | 碩士 === 淡江大學 === 物理研究所 === 81 === Consider a hydrogenic system that hyperboliod surfaces of
revolution with impenetrable walls for electrons are boundary
surfaces. In prolate spheroidal coordinate system, we derived
the electron wavefunctions from the Schrodinger equation. Then
from the following conditions, the boundary condition and the
wavefunctions cannot be equal to zero everywhere in all space
to find the energy eigenvalues and separate constants of this
system. Normalize the wavefunctions that we had obtained, in
order to evaluate physical quantities that we need, for example
the electron probability density at the nucleus, dipole moment,
nuclear magnetic shielding and polarizality. Draw out the
diagrams each physical quantity versus distance and the planar
equivalence diagram of the electron probability density. From
the wavefunctions in the limiting case of xy plane we obatined
that we can realize the probable shapes of these planar
equivalence diagrams. From the figures energy versus distance,
we found if there are some convexitits on a surface when some
atom approaches the surface that this atom has larger
probability to attach the convexitity because this atom has
lower energy in the convexitity than in the concavity. This
phenomenon likes crystal growth. From the figures dipole moment
versus distance, diamagnetic screening constant versus
distance, polarizality versus distance and the electron
probability density at the nucleus versus distance, we can look
out the varieties of these physical quantities and explore the
varing reasons of these ones. If the distance from the atom to
the top of hyperboloid surfaces of revolution is unchanged but
the shape of boundary surfaces and the distance from the atom
to xy plane have changed, from these figures we can look out
the varieties of these physical quantities to understand the
qulitity of these ones under these boundary surfaces.
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