Recursive Generation of The Semi-Classical Expansion in Arbitrary Dimension
arXiv:2012.06041 · doi:10.1103/PhysRevD.103.085011
Abstract
We present a recursive procedure, which is based on the small time expansion of the propagator, in order to generate a semi-classical expansion of the \textit{quantum action} for a quantum mechanical potential in arbitrary dimensions. In the method we use the spectral information emerges from the singularities of the propagator on the complex plane, which are handled by the $i\ve$ prescription and basic complex analysis. This feature allows for generalization to higher dimensions. We illustrate the procedure by providing simple examples in non-relativistic quantum mechanics.
arXiv comment19 pages. v2. Published version. Typos corrected, one reference added
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