(a) Sketch out the first five eigenstates of the particle in a box. Do you notice any symmetry in the center of the box? Comment. 

(Hint: In general, there are two different kinds of functions, based on symmetry about the center. Do you see this? Comment.)

(b) As increases the difference between neighboring energy levels increases. Prove this statement. 

Hint: Calculate(En+1−En). What happens to this expression increases? How about when does to infinity?