Time Evolution Exercise #5

Please answer the  following 6 questions regarding the Physlet:

Description

The superposition shown---both Y_n1n2 and Y_n1n2^* x Y_n1n2---is an equal mix of the two states n₁ and n₂ for the infinite square well, Y_n1n2(x,t)=(1/2)^-1/2 [f_n1 (x,t) + f_n2 (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 Dp at t=0?
2. For n₁ = 1 n₂ = 2, what is Dp at t=0.083 (1/12)?
3. For n₁ = 1 n₂ = 2, what is Dp at t=0.166 (1/6)?
4. For n₁ = 1 n₂ = 2, what is Dp at t=0.250 (1/4)?
5. For n₁ = 1 n₂ = 2, what is Dp 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