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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.

Solution :-Normalization of the wavefunction:The wavefunction must be normalized such that the probability of finding the particle anywhere in the box