please help me with these questions. please explain 1, 3 and 4

3. Consider a system whose wave function at time t = 0 is given by y(x, 0) = 40(x) + 91(x) +793(x), where On (x) is the wave function of the oth excited state for a harmonic oscillator of energy En = hw(n + 1/2). a.) Find the average energy of this system. b.) Find the state (x, t) at a later time t and the average value of the energy; compare the result with the value obtained in (a). C.) Find the expectation value of the operator X with respect to the state (x, t). 4. If the state of a particle moving in a one-dimensional harmonic oscillator is given by 1 3 2 10) + [1) - 13) V17 V17 V17 12) 17 where In) represents the normalized oth energy eigenstate, find the expectation values of the number operator, N , and of the Hamiltonian operator.1. Using the uncertainty principle, show that the lowest energy of an oscillator is hZw