Harmonic oscillator and ladder operators (12 points) Suppose that we have a particle of mass
m
constrained to move on a circle of radius a. (a) What is the Hamiltonian of such a particle? (b) write down the Hamiltonian based on the ladder operators
a^(+)
and
a
, (c) Please calculate its eigenvalues
E_(n)
for the
n_(th)
eigenvector.