Consider an infinite potential well with potential zero between 0 < r < a and infinite elsewhere. The energy eigenfunctions are given as o,() = sin with energy eigenvalues En = nE,, where n= 1,2, 3. and E, = 2ma Let the particle confined in this potential is prepared in the state given by the normalized wavefunction, 15 {: 4b (x) =- 8ab a2 elsewhere where b is a constant. (a) (5 points) Calculate the average energy of the particle in terms of E,. (b) (10 points) Lets say we perform the energy measurement. By calculating the probabilities of the energy outcomes E and E2, discuss in which of the two energy states, particle is more likely to be found after the measurement.