A particle of mass m in a one-dimensional harmonic oscillator is initially in a state given by 亚(0)) 1 (|1) – |2)) where |n) are the time-independent eigenstates of the harmonic oscillator with corresponding energy eigenvalues En = ħw(n + }). (a) If one were to measure the energy of the particle in such state, what values would one get and what would be their associated probabilities? (b) Evaluate the time-dependent expectation values (r(t)) and (r²(t)) and from your results evaluate Ar = V(z?(t)) – (x)²

A particle of mass m in a one-dimensional harmonic oscillator is initially in a state given by 亚(0)) 1 (|1) – |2)) where |n) are the time-independent eigenstates of the harmonic oscillator with corresponding energy eigenvalues En = ħw(n + }). (a) If one were to measure the energy of the particle in such state, what values would one get and what would be their associated probabilities? (b) Evaluate the time-dependent expectation values (r(t)) and (r²(t)) and from your results evaluate Ar = V(z?(t)) – (x)²