An electron is restricted to a one$-$dimensional box, where the potential energy U$($x$)=0$ for $$L$/2<$ x $<$ L$/2($and is essentially infinite for any other value of x$).$ The wave function of the electron is equal to $0$ outside of the box and is a sinusoidal function inside of the box. a$)$ Write expressions for the wave function for n $=1$ and n $=6.$ Be sure to include the correct normalization constant for the functions. $($Use the following as necessary: x and L$.)$ b$)$If the wave function satisfies Schr$$dinger$\text{'}$s equation and L $=0\mathrm{.}125$ nm$,$ determine the energy $($in eV$)$ of the electron for n $=6.$