A quantum mechanical particle with mass m is placed in a potential well with the potential energy of V(x) = Zmzxz, where [3' is a constant with the appropriate unit. For all the questions below, your result should NOT contain at. a) Write down the normalized wavefunction for the lowest energy level that this particle can be on (i.e., nd |0)). b) Using ladder operators. calculate the normalized wavefunction for the energy level with an energy of S. c) Show that the two wavefunctions in parts (a) and (b) are orthogonaL