A particle of mass m is in a one-dimensional infinite square well potential of length a given by a) = { (0SIS4) V (r) = 00, elsewhere The particle is in a state such that a measurement of the energy yields either E 25% of the time E2 75% of the time. Here, En = an? are the energy eigenvalues of the particle in the well. 2ma? (a) Write down the normalized time-dependent wave function of the particle. (b) Find the time dependence of the expectation value of the position of the momentum of the particle Zp(t)). Is it constant in time? (c) Evaluate the probability density p(x, t) = |v(x, t)|². Is it time-independent?

A particle of mass m is in a one-dimensional infinite square well potential of length a given by a) = { (0SIS4) V (r) = 00, elsewhere The particle is in a state such that a measurement of the energy yields either E 25% of the time E2 75% of the time. Here, En = an? are the energy eigenvalues of the particle in the well. 2ma? (a) Write down the normalized time-dependent wave function of the particle. (b) Find the time dependence of the expectation value of the position of the momentum of the particle Zp(t)). Is it constant in time? (c) Evaluate the probability density p(x, t) = |v(x, t)|². Is it time-independent?