[6] 7. Write the Heisenberg equation of motion for a Heisenberg operator
hat(A)_(H)
which does not depend explicitly on time. Determine the equations of motion for the operator
(:hat(x):)
and
(:hat(P):)
for a particle of mass
m
in a gravitational field with the Hamiltonian
hat(H)=(hat(P)^(2))/(2m)+mghat(x)
. Solve the equations of motion to get
hat(x)(t)
and
hat(P)(t)
, using the conditions