Let the particle is confined in an infinite potential well and particle wavefunction is given by, Y (x, 0) = 9:(x) + i92(x) + Ae-l@3(x) ta@3(x) where a is real and constant. The o1 (x),9 2 (x) and o 3 (x) are the orthonormal energy eigenfunctions corresponding to energies E. ,4E. and 9E. respectively. (a) (5 points) Find out the constant A using the normalization condition for u(x, 0). (b) (5 points) Let say we perform an energy measurement on the given state of the system. What are the possible outcomes of the energy measurements and what are the corresponding probabilities? Give proper mathematical justification.