Consider a particle of mass m in a box of length a, where the position (x) is defined by 0?x?a. The system is prepared such that the wavefuntion is given by ?(x)=Ax2(a?x).
Find a value of A that normalizes the wave function.
Plot the wavefunction.
You may wish to use Excel or a suitable program to do this.
Calculate the expectation value of energy <E> for the system.
Calculate the expectation value of position <x> for the system.
Discuss whether or not your results for parts C and D are what you expected and/or are reasonable.