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Revista mexicana de física
versión impresa ISSN 0035-001X
Resumen
ROJAS, R.A. y 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 17-Abr-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, , , , and the critical cage radius, as a function of 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 , while others are identified to give bad results in general. The cut-off functions that give, on average, better results are of the form , , 2, 3.
Palabras llave : Confined hydrogen atom; cut-off function; Dirichlet boundary conditions; 31.15.B; 31.15.ac; 31.15.xt.