Role of the cut-off function for the ground state variational wavefunction of the hydrogen atom confined by a hard sphere
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R.A. Rojas [1] ; N. Aquino [1]
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[1] Universidad Autónoma Metropolitana-Iztapalapa, Ciudad de México, México
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- Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 65, Nº. 2, 2019, págs. 116-123
- Idioma: inglés
- Enlaces
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Resumen
A variational treatment of the hydrogen atom in its ground state, enclosed by a hard spherical cavity of radius R_(c), 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 Rc 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.
