Superposition Exercise #1

Please answer the  following 3 questions regarding the Physlet:

n1 =         n2 =    
Start =   End =

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*Psi and the result of the integral.  You can change the limits of integration by typing in the text boxes and clicking the change state button.

Questions

a.  What is the normalization condition?

b.  Vary n1 and n2, keeping n1<n2 to avoid duplicating states and also avoiding n1=n2.  Vary the quantum numbers from 1 to 10.  Do you notice anything special about certain values of n1 and n2?

c.  For n1 =1 and n2 =2, what are the probabilities of finding the particle in the left and right halves of the well?

Credits

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