cusp condition
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2019 ◽  
Vol 65 (2) ◽  
pp. 116 ◽  
Author(s):  
R.A. Rojas ◽  
And N. Aquino

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, <r^-1>,<r>, <r^2>, and the Shannon entropy, and  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 Rc , 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/Rc)^n), n=1,2,3


2006 ◽  
Vol 124 (12) ◽  
pp. 124107
Author(s):  
Min Sung Kim ◽  
Sung-Kie Youn ◽  
Jeung Ku Kang

2005 ◽  
Vol 404 (1-3) ◽  
pp. 156-163 ◽  
Author(s):  
Peter T.A. Galek ◽  
Nicholas C. Handy ◽  
Aron J. Cohen ◽  
Garnet Kin-Lic Chan
Keyword(s):  

2004 ◽  
Vol 389 (1-3) ◽  
pp. 209-211 ◽  
Author(s):  
Krzysztof Pachucki ◽  
Jacek Komasa

2003 ◽  
Vol 118 (6) ◽  
pp. 2491 ◽  
Author(s):  
Victor M. Rosas-Garcia ◽  
T. Daniel Crawford
Keyword(s):  

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