Q1 (10 points) Suppose that the Hamiltonian of a two-state system is written as H = hw where w is a known constant. (a) Find the energy eigenvalues of this system, En, as real numbers. Show calculations. (b) Find the energy eigenstates of this system, Xn, as 2D vectors. Show calculations. (c) Suppose that a particle has the initial wavefunction ult=o = A ( ). Express this wavefunction as a linear combination of the energy eigenstates. Note that you need to find the constant A first. (d) Find the wavefunction of the particle at any time t