# Propagator of a eigenstate

1. Aug 12, 2007

### ehrenfest

If you use propagator formalixm to calculate the future time dependence of a state that starts in an eigenstate, what happens?

The equation for the propagator is

$$K(x, x';t,0) = \sum_n \psi_n^*(x')\psi_n(x)e^{-iE_nt/\hbar$$

So if we start in an eigenstate does that mean that the summation

$$\sum_n \psi_n^*(x')\psi_n(x)e^{-iE_nt/\hbar$$

can be rewritten

$$\sum_n \psi_n^*(x')\psi_9(x)e^{-iE_nt/\hbar$$

say if we started in the eigenstate corresponding to n = 9?