Superposition of Infinite Square Well States

Description

This is a question related to a superposition of states.   Specifically it asks you to normalize the superposition.  However, because of the statement of the problem,  students must first determine that the wave function is a superposition.  Then students must decide how to proceed.  This example highlights the difference between a_n and the fraction of the wave function that is in a particular state. 

Questions

The above wave function Psi, in the upper right-hand graph, is for a particle in an infinite square well of length a = 2.  You may import a function, f(x), and check the overlap integral with the wave function.  

1. The state is not normalized.  Normalize the state and report the properly normalized wave function. You may check here for examples of the proper syntax.

Answers

1. To normalize:   a₁ = sqrt(1/6)   a₃ = sqrt(1/6)   a₅ = sqrt(4/6)

Features of this Script

Uses three graphs and the Filter applet to do the integrals.  

Required Resources

Jar files: DataGraph4_.jar,DataTable4_.jar,Filters4_.jar,STools4.jar

Credits

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