Calculation of electronic and response properties of a hydrogen atom in soft confinement potential: A variational approach

Abstract The electronic properties of atoms confined in finite or infinite boxes with discontinuity have been extensively studied by the researchers. Recently, a smooth or continuous versions of such confining potentials given by $V_{conf}(r) = \left ( \frac{r}{R}\right)^{N}$ with stiffness parameter $N$ and confinement radius $R$ have been considered. This soft-potential coincides with the infinite discontinuous hard-wall potential as $N\longrightarrow\infty$. In this paper, we study the electronic properties of a hydrogen atom confined in a soft-potential using variational approach. For this purpose, we construct the variational wave functions representing ground state as well as few low-lying excited states. The variational wave functions yield quite accurate results for wide range of values of $R$ and $N$. We also employ the variational ground-state wave function to calculate dipole polarizability $\alpha$ and van der Waals coefficient C$_{6}$.