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arXiv · 2012.06041

Recursive Generation of The Semi-Classical Expansion in Arbitrary Dimension

Cihan Pazarbaşı
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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 $t$ 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.

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Cihan Pazarbaşı. 2021-05-07. Recursive Generation of The Semi-Classical Expansion in Arbitrary Dimension. https://doi.org/10.1103/physrevd.103.085011

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