3. Consider a particle in a one-dimensional potential well V(x) = ax^{100} with a > 0. Show that the eigen-
states are also eigenstates of parity. If the energies of the ground, first excited, and second excited
states are denoted by E_0, E_1, and E_2 respectively, find an approximate value of (E_2-E_1)/(E_1 - E_0).
Check whether the ground state wavefunction is real.