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Determination of the helium atom ground state through the Hamilton–Jacobi equation
Author(s) -
Nascimento D. L.,
Fonseca A. L. A.,
Portilho O.
Publication year - 2005
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20591
Subject(s) - helium atom , ground state , helium , quantization (signal processing) , atom (system on chip) , quantum , quantum mechanics , hamilton–jacobi equation , physics , limit (mathematics) , ion , atomic physics , mathematical physics , mathematics , classical mechanics , mathematical analysis , computer science , algorithm , embedded system
We provide a new analysis of the helium atom problem using Hamilton–Jacobi classical theory combined with the Sommerfeld quantization rule. The study is performed by reducing the three‐body problem to an effective one‐body problem, and it is shown that the theory is capable of reproducing (with a precision of 2%) the atomic ground‐state binding energy. We have also obtained the exact asymptotic limit for the ground state of the helium ion. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005