Delay time and phase of the initial state
The study presented in this paper is intended to show how to calculate the average delay time of a scattering within the framework of the delay time operator Q in order to prove that the average delay time is independent from the phase of the initial state. This conclusion differs from Ohmura's assertion in a recent paper that in the three-dimensional scattering, the average delay time depends on the phase change of the initial state. Our result saves the hope that the delay time of a collision can be known in terms of the S matrix alone. The reason for the difference between our result and Ohmura's is also discussed. We also investigate the commutation of the Q and S matrices and search for the interesting consequences of this commutation.