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The usual implement procedure for the reconstruction of secular equation foran effective Hamiltonian has been discussed and improved. A relativecharacteristic polynomial has been introduced for the effective Hamiltonian, toobtain a simplified effective-secular-equation which is equivalent to the oneobtained in the usual reconstruction procedure but shows great convenience andeffectiveness, especially when the $P$-space dimension is large.

Improving procedure for the reconstruction of an effective secular equation