The variational approximation method developed by Bogolyubov et al. is generalized to treat the dynamical problems of superconductor tunneling system, which results in establishing the approximate expressions, in second quantization representation, for the equation of motion, the. Hamiltonian of superconductor tunneling system and the operators of tunneling current in this variational approximation scheme. The Hamil-tonian obtained, H = HL + HR + HT + WT, consists of three parts: HL describes the behaviours of the metal on the left hand side of the sample; while HR the behaviours of the metal on the right hand side; and HT+WT the coupling between them. HL and HR are commutable with each other, and their expressions are the same as two isolating metals, except that the states of single electron are slightly mixed. The formula of matrix elements of HT is identical with that of Bardeen. The effect of WT is approxi-mately 10000 times less than that of HT, hence WT may be neglected. It is demonstra-ted that as far as the first order terms in our variational approximation method is con-cerned, the model Hamiltonian assumed by Cohen et al. applies, while Prange's treat-ment for this problem is proved to be inappropriate.
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