  The classical time of arrival in the interacting case is quantized by way of
quantizing its expansion about the free time of arrival. The quantization is
formulated in coordinate representation which represents ordering rules in
terms of two variable polynomial functions. This leads to representations of
the quantized time of arrival operators as integral operators whose kernels are
determined by the chosen ordering rule. The formulation lends itself to
generalization which allows construction of time of arrival operators that
cannot be obtained by direct quantization using particular ordering rules. Wey,
symmetric and Born-Jordan quantizations are specifically studied. The dynamics
of the eigenfunctions of the different time of arrival operators are
investigated. The eigenfunctions exhibit unitary arrival at the intended
arrival point at their respective eigenvalues.
