- #1
the1ceman
- 28
- 0
Homework Statement
The Lagrangian of a non-relativistic particle propagating on a unit circle is
[tex]
L=\frac{1}{2}\dot{\phi}^{2}
[/tex]
where ϕ is an angle 0 ≤ ϕ < 2π.
(i) Give the Hamiltonian of the theory, and the Poisson brackets of the ca-
nonical variables. Quantize the theory by promoting the Poisson brackets into
commutators, and write the angular momentum operator, L, which is the con-
jugate (momentum) variable of ϕ, in the position representation. Note that in
the position representation
[tex]
\hat{\phi}|\phi\rangle=\phi|\phi\rangle\;,\;\langle\phi'|\phi\rangle=\delta(\phi'-\phi)
[/tex]
Homework Equations
3. The attempt
i am stuck on the part where i have to write down L, how do i find its form in the $\phi$ representation? Please help