We work out the problems of the spherical harmonics and the monopole harmonics using a representation of the Cartesian co-ordinates and the corresponding linear differential operators with the guidance of the Dirac brackets. This formalism reveals the rotational symmetry better than that using the angular variables.。
We present an exposition explaining the implication of the Dirac bracket as well as its application to derive equations of motion in the full phase space for some simple dynamical systems in classical mechanics.。
