Abstract

ROJAS, R.A.  and  AQUINO, N.. Role of the cut-off function for the ground state variational wavefunction of the hydrogen atom confined by a hard sphere. Rev. mex. fis. [online]. 2019, vol.65, n.2, pp.116-123.  Epub Apr 17, 2020. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.65.116.

A variational treatment of the hydrogen atom in its ground state, enclosed by a hard spherical cavity of radius Rc, is developed by considering the ansatz wavefunction as the product of the free-atom 1s orbital times a cut-off function to satisfy the Dirichlet boundary condition imposed by the impenetrable confining sphere. Seven different expressions for the cut-off function are employed to evaluate the energy, the cusp condition, the Shannon entropy, $⟨r^{-1}⟩$, $⟨r⟩$, $⟨r^2⟩$, and the critical cage radius, as a function of $R_c$ in each case. We investigate which of the proposed cut-off functions provides best agreement with available corresponding exact calculations for the above quantities. We find that most of these cut-off functions work better in certain regions of $R_c$, while others are identified to give bad results in general. The cut-off functions that give, on average, better results are of the form $(1-(r/R_c{)}^n)$, $n=1$, 2, 3.

Keywords : Confined hydrogen atom; cut-off function; Dirichlet boundary conditions; 31.15.B; 31.15.ac; 31.15.xt.

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