arXiv subjects

H. Olivares-Pilón

Publications and source records attributed to H. Olivares-Pilón.

3 recordsLinked to original sources

arXiv2025

Cylindrically confined $H$ atom in magnetic field: variational cut-off factor

In the present study, we consider the hydrogen atom confined within an impenetrable infinite cylindrical cavity of radius $ρ_{0}$ in the presence of a constant magnetic field ${\bf B} = B\,\hat{\bf z}$ oriented along the main cylinder's axis. In the Born-Oppenheimer approximation, anchoring the nucleus to the geometric center of the cylinder, a physically meaningful 3-parametric trial function is used to determine the ground state energy $E$ of the system. This trial function incorporates the exact symmetries and key limiting behaviors of the problem explicitly. In particular, it does not treat the Coulomb potential nor the magnetic interaction as a \textit{perturbation}. The novel inclusion of a variational cut-off factor $\big(1 - \big(\fracρ{ρ_0}\big)^ν\big)$, $ν\geq 1$, appears to represent a significant improvement compared to the non-variational cut-off factors commonly employed in the literature. The dependence of the total energy $E=E(ρ_0,\,B)$ and the binding energy $E_b=E_b(ρ_0,\,B)$ on the cavity radius $ρ_0 \in [0.8,\,5] \,$a.u. and the magnetic field strength $B\in [0.0,\,1.0]\,$a.u. is presented in detail. The expectation values $\langle ρ\rangle$ and $\langle|z| \rangle$, and the Shannon entropy in position space are computed to provide additional insights into the system's localization. A brief discussion is provided comparing the 2D and 3D cases as well.

quant-ph↗

arXiv2022

3-body harmonic molecule

In this study, the quantum 3-body harmonic system with finite rest length $R$ and zero total angular momentum $L=0$ is explored. It governs the near-equilibrium $S$-states eigenfunctions $ψ(r_{12},r_{13},r_{23})$ of three identical point particles interacting by means of any pairwise confining potential $V(r_{12},r_{13},r_{23})$ that entirely depends on the relative distances $r_{ij}=|{\mathbf r}_i-{\mathbf r}_j|$ between particles. At $R=0$, the system admits a complete separation of variables in Jacobi-coordinates, it is (maximally) superintegrable and exactly-solvable. The whole spectra of excited states is degenerate, and to analyze it a detailed comparison between two relevant Lie-algebraic representations of the corresponding reduced Hamiltonian is carried out. At $R>0$, the problem is not even integrable nor exactly-solvable and the degeneration is partially removed. In this case, no exact solutions of the Schrödinger equation have been found so far whilst its classical counterpart turns out to be a chaotic system. For $R>0$, accurate values for the total energy $E$ of the lowest quantum states are obtained using the Lagrange-mesh method. Concrete explicit results with not less than eleven significant digits for the states $N=0,1,2,3$ are presented in the range $0\leq R \leq 4.0$~a.u. . In particular, it is shown that (I) the energy curve $E=E(R)$ develops a global minimum as a function of the rest length $R$, and it tends asymptotically to a finite value at large $R$, and (II) the degenerate states split into sub-levels. For the ground state, perturbative (small-$R$) and two-parametric variational results (arbitrary $R$) are displayed as well. An extension of the model with applications in molecular physics is briefly discussed.

quant-ph↗

arXiv2022

Hydrogen atom confined inside an inverted-Gaussian potential

In this work, we consider the hydrogen atom confined inside a penetrable spherical potential. The confining potential is described by an inverted-Gaussian function of depth $ω_0$, width $σ$ and centered at $r_c$. In particular, this model has been used to study atoms inside a $C_{60}$ fullerene. For the lowest values of angular momentum $l=0,1,2$, the spectra of the system as a function of the parameters ($ω_0,σ,r_c$) is calculated using three distinct numerical methods: (i) Lagrange-mesh method, (ii) fourth order finite differences and (iii) the finite element method. Concrete results with not less than 11 significant figures are displayed. Also, within the Lagrange-mesh approach the corresponding eigenfunctions and the expectation value of $r$ for the first six states of $s, p$ and $d$ symmetries, respectively, are presented. Our accurate energies are taken as initial data to train an artificial neural network as well. It generates an efficient numerical interpolation. The present numerical results improve and extend those reported in the literature.

physics.atom-ph↗