Topological recursion of Eynard-Orantin and the Harmonic Oscillator

Abstract

We apply the Chekhov-Eynard-Orantin topological recursion to the curve corresponding to the quantum harmonic oscillator and demonstrate that the result is equivalent to the WKB wave function. We also show that using the multi-differentials obtained by the topological recursion from the harmonic oscillator curve, one generates naturally the so-called Poincaré polynomials associated with the orbifolds of the metric ribbon graphs.

28 pages. Reference [4] to the paper arXiv:1606.04498 added in the second version

References in corpus (3)

• Determinantal formulae and loop equations
• A short overview of the "Topological recursion"
• Intersection numbers on Deligne-Mumford moduli spaces and quantum Airy curve

Cited by in corpus (1)

• A formalism of abstract quantum field theory of summation of fat graphs