a) Show that the particle in a box wavefunctions w = Nsin(ntx/L) with 0 < x

in a box. Why do we write superposition wavefunctions and not just eigenstate wavefunctions? \text { Show that ground state wavefunction of the } \mathrm{H} \text { atom, } \psi=N \exp \left(-r / 2 a_{0}\right) \text {, is orthogonal to the } 2 \mathrm{~s} \text { orbital } \psi=N\left(2-r / a_{0}\right) \exp \left(-r / 2 a_{0}\right) \text { and the } 2 \mathrm{p}_{\mathrm{x}} \text { orbital } \psi=N x \cdot \exp \left(-r / 2 a_{0}\right) Explain why orthogonality is important in creating superposition wavefunctions.