Superposition Exercise #5

Please answer the  following 2 questions regarding the Physlet:

Description

A particle is in a one-dimensional box of length a=1.  It is in a normalized superposition of two states.  There is an equal amount of each state.  Shown is Psi and the results of the integral that give <x> and <x²>.  

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

Questions

1. What do you notice about <x> and <x²>? Do your results differ from the states that were not a superposition of states?
2. For n₁ = 1 n₂ = 2, what is Dx? 

Credits

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