Wednesday, February 15, 2012

1202.3100 (André Voros)

Zeta-regularisation for exact-WKB resolution of a general 1D
Schrödinger equation

André Voros
We review an exact analytical resolution method for general one-dimensional
(1D) quantal anharmonic oscillators: stationary Schr\"odinger equations with
polynomial potentials. An exact form of WKB treatment involves spectral (usual)
vs "classical" (newer) zeta-regularisations in parallel. The central results
are Bohr--Sommerfeld-like but exact quantisation conditions for the
eigenvalues, directly drawn from Wronskian identities, and appearing to extend
Bethe-Ansatz formulae of integrable systems.
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