Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-04-25
Annals Phys. 299 (2002) 143-173
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 8 eps figures
Scientific paper
10.1006/aphy.2002.6272
A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation interchanges bands at the bottom (top) of the spectrum of one potential with gaps at the top (bottom) of the spectrum of the other, dual, potential. Thus, the duality transformation provides an exact mapping between the weak coupling (perturbative) and semiclassical (nonperturbative) sectors.
Dunne Gerald V.
Shifman Michael
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