by introducing the complex canonical coordinates \(z=(x+iy)/ \sqrt{2}\) and \(P=(p_x-ip_y)/ \sqrt{2}\) together their complex conjugate coordinates \( \bar z\) and \( \bar P\ .\) The Hamiltonian is \[H_B= \bar P P+ \omega^2 \bar z z \ . \] This system is quantized through canonical commutation relations. The coordinates satisfy the harmonic