International Journal of Theoretical Physics, Vol. 46, No. 3, March 2007 ( C  2007) DOI: 10.1007/s10773-005-9006-y Total Current Operator and its Classical Correspondence for Particles Bounded in Central Force Fields Q. H. Liu, 1 X. Wang, 1 and Y. B. Yu 1 Received April 8, 2005; accepted November 24, 2005 Published Online: February 22, 2007 When a particle is bounded in a central force field, the only nonvanishing component of the mean value for current density is along the azimuthal direction; and the total current can therefore be defined. It is found that the total current is in fact a mean value of a newly defined total current operator in the quantum mechanical state. Not only the total current operator itself but also the mean total current has exact classical correspondence. KEY WORDS: Quantum mechanics. 1. INTRODUCTION In elementary quantum mechanics, the usual probability density and the usual probability current density come in as two consequences of the fact that the state satisfies Schr¨ odinger equation. As far as we know, it is C. Cohen-Tannoudji, B. Diu, and F. Lal¨ oe who firstly noticed that the probability density and the probability current density are in fact two mean values, in the quantum mechanical state, of the probability density operator ˆ ρ =|x 〉〈x | and probability current density operator ˆ j = (|x 〉〈x | ˆ P + ˆ P|x 〉〈x |)/(2μ), respectively (Cohen-Tannoudji et al., 1977). In this work, we take a similar study and analyze the total current for particles bounded in central force fields. Results show that a total current operator exists in quantum mechanics for particles bounded in central force fields and its classical correspondence is exact. 1 School for Theoretical Physics and Department of Applied Physics, Hunan University, Changsha, 410082, China; e-mail: quanhuiliu@gmail.com. 424 0020-7748/07/0300-0424/0 C  2007 Springer Science+Business Media, Inc.