Hard confinement of a two-particle quantum system using the variational method

The variational method is used to study the hard confinement of a two-particle quantum system in two potential models, the Cornell potential and the global potential, with Dirichlet-type boundary conditions at various cut-off radii. The trial wavefunction is constructed as the product of the $1S$ free hydrogen atom wavefunction or $1S$ free harmonic oscillator wavefunction times a cut-off function of the form $(r-z)$ to ensure hard entrapment within a sphere of radius $z$. The behavior of $|\psi|^2$, the wavefunction at the origin (WFO), and the mean radius $\ev{r}$ are computed for different situations and compared for the two potential models.