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Holomorphic Anomaly and Quantum Mechanics

Number of pages29
Publication date2016
Abstract

We show that the all-orders WKB periods of one-dimensional quantum mechanical oscillators are governed by the refined holomorphic anomaly equations of topological string theory. We analyze in detail the double-well potential and the cubic and quartic oscillators, and we calculate the WKB expansion of their quantum free energies by using the direct integration of the anomaly equations. We reproduce in this way all known results about the quantum periods of these models, which we express in terms of modular forms on the WKB curve. As an application of our results, we study the large order behavior of the WKB expansion in the case of the double well, which displays the double factorial growth typical of string theory.

Classification
  • arxiv : hep-th
NoteSoumis dans : Journal of High Energy Physics
Citation (ISO format)
CODESIDO SANCHEZ, Santiago, MARINO BEIRAS, Marcos. Holomorphic Anomaly and Quantum Mechanics. 2016, p. 29.
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