Generating function approach to quantum-to-classical correspondence I

A method on the generating function, which produces time-evolution equations for moments of coordinate and momentum, is presented to study quantum-to-classical correspondence. A time-evolution equation for the quantal generating function is derived, which reduces to a classical one in the limit h̵ → 0. A quantal analogue of the classical distribution function is defined as the Fourier transform of the generating function. The quantal correction of the generating function is discussed. The relation between a stationary generating function and the energy eigenstates is discussed.