Abstract
The Bose‐Einstein condensation (BEC) has been found for various alkali‐metal gases such as 7Li, 87Rb, Na, and H. For the description of atoms in this condensate state, the Gross‐Pitaevskii (GP) equation has been widely used. However, the GP equation contains the nonlinear term, which makes this equation hard to solve. Therefore, physical quantities are usually obtained numerically, and sometimes it is difficult to extract a physical meaning from the calculated results. The nuclear theory group at Purdue University in the U.S. developed a new simple equation, the equivalent linear two‐body (ELTB) equation, using the hyper‐radius coordinates and tested it for one‐dimensional BEC system. Their results are consistent with the numerical values from the GP equation within 4.5%.We test the validity of the ELTB equation for three‐dimensional BEC system by calculating the energies per particle and the wave functions for 87Rb gas and for 7Li gas. We use the quantum‐mechanical variational method for the BEC energy. ...
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