Generating Function and a Rodrigues Formula for the Polynomials in $d$-Dimensional Semiclassical Wave Packets
George A. Hagedorn
TL;DR
This paper derives a generating function and Rodrigues formula for polynomials in d-dimensional semiclassical wave packets, providing a new mathematical framework for analyzing these quantum states.
Contribution
It introduces a simple generating function formula and proves the Rodrigues formula for polynomials in d-dimensional semiclassical wave packets, advancing theoretical understanding.
Findings
Derived a simple generating function for the polynomials.
Proved the Rodrigues formula for these polynomials.
Provides a new mathematical tool for semiclassical analysis.
Abstract
We present a simple formula for the generating function for the polynomials in the --dimensional semiclassical wave packets. We then use this formula to prove the associated Rodrigues formula.
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Taxonomy
TopicsQuantum optics and atomic interactions · Nonlinear Photonic Systems · Quantum chaos and dynamical systems