Find the integral.

## Time Evolution Exercise #4

 n1 =      n2 =

#### Description

The superposition shown---both Yn1n2 and Yn1n2* x Yn1n2---is an equal mix of the two states n1 and n2 for the infinite square well, Yn1n2(x,t)=(1/2)-1/2 [fn1 (x,t) + fn2 (x,t)].  The wave function evolves with time according to the TDSE.  You may change state by choosing an n1 and n2.  Time is shown in units of the revival time for the ground state wave function of a particle in an infinite square well.  In other words, it is the time for the ground state wave function to undergo a phase change of 2p

#### Questions

Vary n1 and n2 keeping n1<n2 to avoid double counting and also avoid n1=n2.  Vary the quantum numbers from 1 to 10.

1. For n1 = 1 n2 = 2, what is Dx at t=0?
2. For n1 = 1 n2 = 2, what is Dx at t=0.083 (1/12)?
3. For n1 = 1 n2 = 2, what is Dx at t=0.166 (1/6)?
4. For n1 = 1 n2 = 2, what is Dx at t=0.250 (1/4)?
5. For n1 = 1 n2 = 2, what is Dx at t=0.333 (1/3)?
6. What do you recognize from this pattern and by looking at the wave function?

#### Credits

Script by Mario Belloni and Wolfgang Christian.
Questions by Mario Belloni.
Java applets by Wolfgang Christian