For a simple harmonic oscillator, the Lagrangian is given by
\(L=\frac{1}{2} \dot{q}^2-\frac{1}{2} q^2\)
If H(q, p) is the Hamiltonian of the system and \(A(p, q)=\frac{1}{\sqrt{2}}(p+i q)\), the Poisson bracket {A, H} is
1
iA
2
A*
3
-iA*
4
-iA
For a simple harmonic oscillator, the Lagrangian is given by
\(L=\frac{1}{2} \dot{q}^2-\frac{1}{2} q^2\)
If H(q, p) is the Hamiltonian of the system and \(A(p, q)=\frac{1}{\sqrt{2}}(p+i q)\), the Poisson bracket {A, H} is