Question

Quantum Question:

Equation of Motion in Heisenberg picture.

A particle of mass m is in a harmonic oscillator potential with spring constant k. An observable quantity is given in the Schrodinger picture by the operator:

Z=a†aa†a

a) Determine the equation of motion of the operator in the Heisenberg picture

b) Solve the equation of motion to calculate the form of Z as a function of time.

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Answer 1

did you try
\[H=\hbar\omega(a^\dagger a+1/2)\]
in
\[i\hbar \frac{dZ}{dt}=[Z,H]\]