Superposition Exercise #3

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 are Psi and the results of the integrals that give <x> and <x²>.  

Vary n₁ and n₂, keeping n₁<n₂ to avoid duplicating states and also avoiding n₁=n₂.  Vary the quantum numbers from 1 to 10. 

Questions

a. What do you notice about <x> and <x²>?  How do your results differ from states that were not superpositions?

b.  For n₁ = 1, n₂ = 2, what is Dx? 

Credits

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