A formalism where Hamiltonian is generally diagonalised is given and the relation of this formalism to the Tamm-Dancoff equation is studied. The Tamm-Dancoff equation in which the energy of the system appearing in the denominator of the equation is eliminated, can be obtained from the solution of a differential equation. In this energy-eliminated Tamm-Dancoff equation, the subtraction of closed loops is possible. Furthermore, some applications are given.
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Susumu Ôkubo (1954) studied this question.