Assume that at time t 0, the wave function of a particle in an infinite square well potential (ie., v(a)0 if 0 x a, and v(x) energy eigenstates, (x,0) a(1 (x) ib2(x)) =00 otherwise) is given by a superposition of the two lowest (a) from the normalisation condition for(x, 0), find a note that other equivalent and commonly used shortcut terms for this task are (r, 0)", which actually refers to normalising the probability density (r, 0)2) such that the wavefunction is normalised". (a) "normalise (b) "find a or (b) using this initial state, find (r, t) and the probability density (xr, t)2; is the latter corre- sponds to a stationary state? (c) what is the expectation value of the energy for the wave function v(x, t); how does it compare with ei and e2? (d) if i make a measurement of the energy of the particle, what are the possible values that i might get, and what is the probability of getting each of them?