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Physical Review A

Reply to “Comment on ‘Family of modified contracted Schrödinger equations’ ”

Diego R. Alcoba, Carmela Valdemoro

Published Jan 27, 2009• 2 citations
Publisher

Abstract

The preceding Comment by Yasuda [Phys. Rev. A 79, 016101 (2009)] on our earlier paper [Phys. Rev. A 64, 062105 (2001)] raises several objections about the modified contracted Schr\"odinger equations (MCSEs) to which we reply here. In his comment, Yasuda also questions the possibility of obtaining the exact solution of the fourth-order MCSE due to its indeterminacy. We maintain the opposite, at least from a theoretical point of view.

DOI
10.1103/physreva.79.016102

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The preceding Comment by Yasuda [Phys. Rev. A 79, 016101 (2009)] on our earlier paper [Phys. Rev. A 64, 062105 (2001)] raises several objections about the modified contracted Schr"odinger equations (MCSEs) to which we reply here. In his comment, Yasuda also questions the possibility of obtaining the exact solution of the fourth-order MCSE due to its indeterminacy. We maintain the opposite, at least from a theoretical point of view.
A family of equations that combines contracted Schr\"odinger equations of different orders is reported here. Attention is focussed on the resulting second order, third order, and fourth order of these modified-contracted Schr\"odinger equations. Some of these equations are self-contained and have as fixed points those corresponding to the full-configuration interaction eigenstates. The indeterminacy, which hindered initially the use of the contracted Schr\"odinger equations, does not formally exist in these equations. Relations linking the lower-order reduced density matrices with the higher-order matrices are exactly incorporated into the modified-contracted Schr\"odinger-equations structure. The cancellation of high-order correlation terms, which is hidden in the contracted Schr\"odinger equations, now takes an explicit form.