Consider a spinless particle of mass m bound by a one-dimensional harmonic potential of spring constant...

 

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Consider a spinless particle of mass m bound by a one-dimensional harmonic potential of spring constant k (equivalently, we can say that the natural frequency of the oscillator is an = √k/m). Suppose that we prepare the system at t=0 such that |y (0)) = (0) where is the momentum operator and [0) is the ground state of the oscillator. a) Evaluate the mean/average value of (the measurements of) the position of the particle at a later time t. b) Interpret your result physically. This interpretation should include the physics behind Eq. (2); be brief and clear. Consider a spinless particle of mass m bound by a one-dimensional harmonic potential of spring constant k (equivalently, we can say that the natural frequency of the oscillator is an = √k/m). Suppose that we prepare the system at t=0 such that |y (0)) = (0) where is the momentum operator and [0) is the ground state of the oscillator. a) Evaluate the mean/average value of (the measurements of) the position of the particle at a later time t. b) Interpret your result physically. This interpretation should include the physics behind Eq. (2); be brief and clear.