# I Inequality for the time evolution of an overlap

1. May 20, 2017

### Dyatlov

2. May 20, 2017

### hilbert2

You should post this in the Homework forum, using the correct question template.

The function $\left<\psi (0)|\psi(t)\right>$ is called an autocorrelation function. You could start by playing with a two-state system where the state space is spanned by only two vectors, and finding out how the autocorrelation function of $a|\psi_1 > + b|\psi_2 >$ depends on how similar in absolute value the coefficients $a,b$ are. $|\psi_1 >$ and $|\psi_2 >$ are the energy eigenstates here.