2. Particle in a box in 1D and Linear Combinations (Points: 6) For a particle of mass m in a box of length L, we have a wavefunction given by (x)=4L2sin(Lx)+2iL2sin(L2x)2L2sin(L4x)+iL2sin(L6x) A (Points: 2) Rewrite the wavefunction in equation 1 as a linear combination of the eigenfunctions l(x) of the Hamiltonian operator: (x)=lcll(x), and identify all the coefficients cl that are non-zero. Make sure that the resulting linear combination is normalized by re-normalizing the coefficients cl if needed. B (Points: 2) Based on your result in part A, if you do a single measurement of the energy for the wavefunction in equation 1, what are the possible energy values (i.e., eigenvalues) you can obtain? What are the corresponding probabilities? C (Points: 2) Based on your result in part A, calculate the expectation value of the energy E for the wavefunction in equation 1. You should give your answer in terms of 8mL2h2 (you do not need to know the values of m and L)