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

• URL: http://arxiv.org/abs/2402.10788v1
• Date: Fri, 16 Feb 2024 16:12:08 GMT
• Title: Hard confinement of a two-particle quantum system using the variational method
• Abstract summary: The method is used to study the hard confinement of a two-particle quantum system in two potential models. The behavior of $|psi|2$, the wavefunction at the origin (WFO), and the mean radius $evr$ are computed for different situations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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