In this thesis, we investigate physical properties of various atomic systems such
as hydrogen, helium and argon confined in a soft–wall potential of the form
Vs(r) = (r=r0)N ; where r0 is the radius of the spherical confinement and N is the
stiffness controlling variable. Our main purpose is to introduce a confinement
for atomic systems that is flexible in terms of sti ness of the confining walls.
However, this brings its complications such as non–existence of analytic solutions
to the non–relativistic Schr¨odinger equation for this particular problem, and non–
availability of good basis sets for studying electronic properties of such systems.
Therefore, at first, we treat the problem in pure numerical fashion. Based on our
experience on the numerical data, we then attempt to design basis sets that can be
used in quantum chemical software packages. We compare our results to known
theoretical and experimental results and, in return, make a decision on the quality
of the basis sets. To our knowledge, systems confined in this type of potential has
not yet been studied, and, we believe that this study will open up new research
areas in this field. Possible applications are in high–pressure simulations of atomic,
or molecular systems.