A Quantized Hill's Dynamical System

In this paper, we present a modified version of Hill's dynamical system that is called the quantized Hill's three-body problem in the sense that the equations of motion for the classical Hill's problem are now derived under the effects of quantum corrections. To do so, the position variables and the parameters that correspond to the quantum corrections of the respective quantized three-body problem are scaled appropriately, and then by taking the limit when the parameter of mass ratio tends to zero, we obtain the relevant equations of motion for the spatial quantized Hill's problem. Furthermore, the Hamiltonian formula and related equations of motion are also derived.

Automated summary

This paper introduces a modified version of Hill's dynamical system, known as the quantized Hill's three-body problem, where the equations of motion for the classical Hill's problem are derived under the effects of quantum corrections. By appropriately scaling position variables and corresponding parameters, the relevant equations of motion for the spatial quantized Hill's problem are obtained when the mass ratio parameter tends to zero. Additionally, the Hamiltonian formula and related equations of motion are derived.