对建立约瑟夫森方程的费因曼模型严格解

Exact Solutions to the Feynman Model Establishing the Josephson Equations

费因曼模型是建立约瑟夫森方程的著名理论模型．费因曼等人以描写超导体结的二态系统的薛定谔方程为基础，推导出二种波函数的幅度、相位对时间的微分方程，使用了较粗糙的方法求解这些微分方程，建立起约瑟夫森方程．值得认真考虑的是，费因曼模型中的数学处理是不够严格的．本文严格求解了模型中的微分方程，得到的结果表明，只有在一定条件下才能建立起交流约瑟夫森方程．

The Feynman model is a famous theoretical model establishing the Josephson equations. Feynman et al. based on the Schrodinger equations describing the two states system of superconductor junction, have derived the differential equations of the amplitudes and phases of the two wave functions versus time, and solved them with a slightly rough method, and established the Josephson equation. It is worth considering carefully that mathematical treatment in Feynman model was not exact. In this paper we have solved the differential equations in Feynman model exactly, the results we have gotten show that A. C. Josephson equations can be established only under certain conditions..