## Superposition Exercise #1

#### Please answer the following 3 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^{*}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 n_{1} and n_{2}, keeping n_{1}<n_{2}
to avoid duplicating states and also avoiding n_{1}=n_{2}. Vary
the quantum numbers from 1 to 10. Do you notice anything special about certain
values of n_{1} and n_{2}?

c. For n_{1} =1 and n_{2} =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.