Quantization of the double pendulum

Abstract

The double pendulum is one of the best tools for demonstrating classical chaos and yet its quantization has somehow escaped attention. An attempt is made to fill this gap. We show that the constraint-induced Riemann curvature scalar plays an important role in the proper quantization and evaluation of the energy spectra of this system. The quantum energies are compared with the semiclassical results obtained earlier by resumming the Birkhoff–Gustavson normal form series. The general agreement between the two sets of energies demonstrates how a proper resummation makes it possible to use a divergent normal form series for semiclassical analyses.