a) Show that the particle in a box wavefunctions = Nsin(nnx/L) with 0 < x< L are orthogonal to each other b) Write a superposition wavefunction for the particle in

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