ABSTRACT
Potential (AQP) ............................................................................................138 9.3 AQP Dynamics with Balanced Approximation Errors..................................141 9.4 Conclusions...................................................................................................146 Acknowledgments..................................................................................................148 Bibliography ..........................................................................................................148
In this chapter we justify and explain the use of a semiclassical approach in quantum trajectory dynamics, then show how approximations can be balanced to make the dynamics stable in time. For simplicity, derivations of Sections 9.1 and 9.2 are given for one-spatial dimension x for a particle of mass m. Arguments of functions are omitted where unambiguous. Differentiation with respect to x is denoted as ∇. Differentiation with respect to a variable other than x is indicated with a subscript. The multidimensional generalization to an arbitrary coordinate system is given in Ref. [1].
