Equation of Motion for the Quantum Characteristic Functions

Details Equation of Motion for the Quantum Characteristic Functions Equation of Motion for the Quantum Characteristic Functions

2008-03-02

arxiv.org/abs/0803.0108v2

Physics

Quantum Physics

5 pages

Scientific paper

In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form' of both quantum states and Hamiltonians. The equations of motion we derive here are rather simple in form and in essence, and as such have a number of attractive features. As we shall see, our approach enables the descriptions of quantum and classical time evolutions in one unified language. It allows for a direct comparison between quantum and classical dynamics, providing insight into the relations between quantum and classical behavior, while also revealing a smooth transition between quantum and classical time evolutions. In particular, the $\hbar\to 0$ limit of the quantum equations of motion instantly recovers their classical counterpart. We also argue that the derived equations may prove to be very useful in numerical simulations.

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