2007•Unpublished venueRequires access
Airy function (exact WKB results for potentials of odd degree)
André Voros, F-- Gif-sur-yvette Cedex (france
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Abstract
] H def = \\Gamma d 2 dq 2 + q N ; for N an even integer. (1) (Obvious dependences upon the parameter N will be left implied.) Over L 2 (R), H is a strictly positive operator; it has a purely discrete (nondegenerate) spectrum f k g k=0;1;2;::: , and k " +1 according to the asymptotic Bohr--Sommerfeld law b 0 ¯ k ¸ 2ß(k + 1=2); k !1 in N; (2) which uses the classical action b 0 ¯ (at the energy , for the Hamiltonian p 2