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.  This example highlights the difference between an 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.

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

References

 

Credits

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