Question

7. A particle of mass M is constrained to move on a circle of radius R on the xy-plane with center at the origin, but is otherwise free. \partial (a) Write the Hamiltonian H in terms of $L_z$, where $L_z = -i\hbar \frac{\partial}{\partial \phi}$. (b) Construct a complete set of simultaneous, orthonormal eigenfunc- tions of H and $L_z$: $f_m(\phi)$, $-\infty < m < \infty$. (c) Write the completeness and orthonormality conditions of this set of eigenfunctions using both the Dirac notation and in terms of the func- tional forms of $f_m(\phi)$.

          7. A particle of mass M is constrained to move on a circle of radius R on
the xy-plane with center at the origin, but is otherwise free.
\partial
(a) Write the Hamiltonian H in terms of $L_z$, where $L_z = -i\hbar \frac{\partial}{\partial \phi}$.
(b) Construct a complete set of simultaneous, orthonormal eigenfunc-
tions of H and $L_z$: $f_m(\phi)$, $-\infty < m < \infty$.
(c) Write the completeness and orthonormality conditions of this set of
eigenfunctions using both the Dirac notation and in terms of the func-
tional forms of $f_m(\phi)$.

7. A particle of mass M is constrained to move on a circle of radius R on
the xy-plane with center at the origin, but is otherwise free.
∂(a) Write the Hamiltonian H in terms of Lz, where Lz = -iħ(∂)/(∂ϕ).
(b) Construct a complete set of simultaneous, orthonormal eigenfunc-
tions of H and Lz: fm(ϕ), -∞ < m < ∞.
(c) Write the completeness and orthonormality conditions of this set of
eigenfunctions using both the Dirac notation and in terms of the func-
tional forms of fm(ϕ).

Added by Anthony R.

Question

Please give Ace some feedback