Solution to the TKE for an arbitrary everywhere analytic potential

Abstract

The solution T(u; v) to the Time Kernel Equation (TKE) is an important function to derive since it gives an explicit form of the Time of Arrival (TOA) operator. For an arbitrary everywhere analytic potential, the kernel factor T(u; v) was determined. It was seen that the quantum corrections can be calculated up to a certain degree with the use of a recurrence relation.