Explicitly solve the Heisenberg equations of motion to find the time–dependent raising and lowering (creation and annihilation) operators for a one-dimensional oscillator in the Heisenberg picture. Show these operators are consistent with the time–dependent position and momentum operators previously derived in Lecture

see detailed solution attached.

Explanation:

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.