The Spectrum of a Harmonic Oscillator Operator Perturbed by Point Interactions
نویسندگان
چکیده
منابع مشابه
Spectral asymptotics of harmonic oscillator perturbed by bounded potential
Consider the operator T = − d dx2 + x2 + q(x) in L2(R), where real functions q, q′ and ∫ x 0 q(s) ds are bounded. In particular, q is periodic or almost periodic. The spectrum of T is purely discrete and consists of the simple eigenvalues {μn}n=0, μn < μn+1. We determine their asymptotics μn = (2n+1)+(2π) −1 ∫ π −π q( √ 2n + 1 sin θ) dθ+O(n−1/3).
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ژورنال
عنوان ژورنال: International Journal of Theoretical Physics
سال: 2015
ISSN: 0020-7748,1572-9575
DOI: 10.1007/s10773-014-2468-z