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We present a recursive procedure, which is based on the small time expansionof the propagator, in order to generate a semi-classical expansion of the\textit{quantum action} for a quantum mechanical potential in arbitrarydimensions. In the method we use the spectral information emerges from thesingularities of the propagator on the complex $t$ plane, which are handled bythe $i\ve$ prescription and basic complex analysis. This feature allows forgeneralization to higher dimensions. We illustrate the procedure by providingsimple examples in non-relativistic quantum mechanics.

Recursive Generation of The Semi-Classical Expansion in Arbitrary Dimension