Airy function (exact WKB results for potentials of odd degree)
Voros, A.
arXiv, 9811001 / Harvested from arXiv
Text on arXiv
An exact WKB treatment of 1-d homogeneous Schr\"odinger operators (with the confining potentials $q^N$, $N$ even) is extended to odd degrees $N$. The resulting formalism is first illustrated theoretically and numerically upon the spectrum of the cubic oscillator (potential $|q|^3$). Concerning the linear potential (N=1), the theory exhibits a duality in which the Airy functions Ai, Ai' become paired with the spectral determinants of the quartic oscillator (N=4). Classic identities for the Airy function, as well as some less familiar ones, appear in this new perspective as special cases in a general setting.
Publié le : 1998-11-02
Classification:  Mathematical Physics,  Mathematics - Classical Analysis and ODEs,  Quantum Physics 
@article{9811001,
     author = {Voros, A.},
     title = {Airy function (exact WKB results for potentials of odd degree)},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9811001}
}

Voros, A. Airy function (exact WKB results for potentials of odd degree). arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9811001/