(Solved): Harmonic oscillator and ladder operators (12 points) Suppose that we have a particle of mass m const ...

Harmonic oscillator and ladder operators (12 points) Suppose that we have a particle of mass

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

and

, (c) Please calculate its eigenvalues

for the

eigenvector.