In this problem we consider a standard harmonic oscillator with hamiltonian н the energy levels given by en hw(n and the 2m eigenstates denoted by n) 11 pts] assume first that the system is in the state |2). what is the probability distribution of the coordinate of the system? to calculate this use а. the wave function of the first excited state given by 2mw тw mw b(x) 2h -те and creation operators. sketch the shape of the probability distribution b. [11 ptsl assume the system is in the ground state |0).what is the proba- bility distribution of the momentum? you can either use the wave function in coordinate representation derived in class or write the creation and annihila- tion operators in momentum representation (ie. express the coordinate operator derivative of momentum such that the canonical commutation relation is as a satisfied) and then solve a first order differential equation for the momentum representation of the wave function 12) 13 pts assume now that the system is in the state will be the state of the system at a later time t? what is the expectation value of 2 at time t = t/w? what c.