
This is a question related to a superposition of states. Specifically it asks you to normalize the superposition. This example highlights the difference between a_{n} and the fraction of the wave function that is in a particular state.
The above wave function, Psi in the upper righthand 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.
To normalize: a_{1} = sqrt(1/6) a_{3} = sqrt(1/6) a_{5} = sqrt(4/6)
Uses three graphs and the Filter applet to do the integrals.
Jar files: DataGraph4_.jar,DataTable4_.jar,Filters4_.jar,STools4.jar
Script by Mario Belloni.
Questions by Mario Belloni.
Java applets by Wolfgang Christian.