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 wave function is constructed as the product of the [Formula: see text] free hydrogen atom wave function or [Formula: see text] harmonic oscillator wave function times a linear cut-off function of the form [Formula: see text] to ensure hard entrapment within a sphere of radius z. The behavior of [Formula: see text], the wave function at the origin (WFO) and the mean radius [Formula: see text] are computed for different situations and compared for the two potential models.