A duality of the classical action yields a reflection symmetry of the quantum energy spectrum
Abstract
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain transformation. We term this phenomenon as the energyspectrum reflection symmetry. We develop an approach to this class of problems, based on the global properties of the Riemann surface of the quantum momentum function, a natural quantummechanical analogue to the classical momentum. In contrast to the algebraic method, which we also briefly review, our treatment provides an explanation to the longnoticed matching of the perturbative and WKB expansions of dual energy levels. Our technique also reveals the classical origins of duality.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 DOI:
 10.48550/arXiv.1603.08962
 arXiv:
 arXiv:1603.08962
 Bibcode:
 2016arXiv160308962K
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 doi:10.1088/17518121/ab3ac2