计算物理第五次作业

夏海峰
学号： 2013301020094
Consider again a decay problem with two types of nuclei A and B, but now suppose that nuclei of type A decay into ones of type B, while nuclei of type B decay into ones of type A. Strictly speaking, this is not a "decay" process, since it is possible for the type B nuclei to turn back into type A nuclei. A better analogy would be a resonance in which a system can tunnel or move back and forth between two states A and B which have equal energies. The corresponding rate equations are:

where for simplicity we have assumed that, the two types of decay are characterized by the same time constant, T. Solve this system of equations for the numbers of nuclei, NA and NE, as functions of time. Consider different initial connditions, such as NA 100, NB O, etc., and take T I s. Show that
your numerical results are consistent with the idea that the system reaches a steady state in which NA and NE are constant. In such a steady state, the time derivatives d,'VA and dNB/dt should vanish.