Please show hand writing work.

Consider a particle in an infinite 1D potential well with width L, which is positioned symmetrically around zero (2Lx2L). A) Using the time-independent Schrdinger equation to solve for the eigenstates of the system. Hint: Unlike the system solved in class, there will be both an even and an odd function, depending on whether n is odd or even. B) Use the position operator x^ and momentum operator p^ to calculate the uncertainty for position x=x^2x^2 and momentum p=p^2p^2 for state n. Show that for any state n, Heisenberg's uncertainty principle must not be violated