As described in class, the poisson bracket [f, g] between two functions f and g of the generalized
positions qi and momenta pi is defined as:
[f, g] = ∑i� ∂f/∂qi ∂g/∂pi- ∂g/∂qi ∂f∂pi
consider a system with hamiltonian h= p2 / 2m - γ/r = (px^2+py^2+pz^2) / (2m) - γ (x ^2 + y^2 + z^2) -1/2
where γ is a constant.
a) evaluate [lz, h] and interpret the result in two ways i. e. what it says about lz, and what it says about
h.
b) using the poisson bracket and the given hamiltonian, find the value of α that makes the quantity
pxl-at a constant of the motion (i. e. invariant in time).