EXERCISE 6.5. Consider a harmonic oscillator with Hamiltonian, = (1/2m)(p2+mw22). Assume that at time = 0 the oscillator is a state described by the density operator, (0) = hab(e-a e-bp + e-bp e-ax), where a and b are constants with the dimensions of inverse length squared and inverse momentum squared, respectively.

(a) Compute the probability to find the particle in the interval xx+ dx at time t = 0.

(b) Write the Liouville equation in the position basis.

(c) Compute the probability to find the particle in the interval x-x+dx at time t.