2013
DOI: 10.1090/s0077-1554-2013-00205-8
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Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters

Abstract: Abstract. We investigate the second-order Zeeman effect in a magnetic field using irreducible representations of an algebra with the Karasev -Novikova quadratic commutation relations. To each such representation there corresponds a spectral cluster near the energy level of the unperturbed hydrogen atom. Using this model as an example, we describe a general method for constructing asymptotic solutions near the boundaries of spectral clusters based on a new integral representation. We also study the problem of c… Show more

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Cited by 2 publications
(5 citation statements)
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References 30 publications
(51 reference statements)
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“…Then Y 1 (1) = Y 0 (1) = 0, the uniqueness theorem, we have Y 1 (z) = Y 0 (z) and arrive at a contradiction. Consequently, Y 0 (1) = 0.As in[3], we show that Φ P[m,n] differs from p P[m,n] by an exponentially small number in comparison with p P[m,n] . Therefore, ifc 0 = I −1/2 , (8.6)where I is given by (8.3), then the normalization condition holds: Φ(z) P[m,n] = 1 + O(|m| −1 ).…”
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confidence: 74%
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“…Then Y 1 (1) = Y 0 (1) = 0, the uniqueness theorem, we have Y 1 (z) = Y 0 (z) and arrive at a contradiction. Consequently, Y 0 (1) = 0.As in[3], we show that Φ P[m,n] differs from p P[m,n] by an exponentially small number in comparison with p P[m,n] . Therefore, ifc 0 = I −1/2 , (8.6)where I is given by (8.3), then the normalization condition holds: Φ(z) P[m,n] = 1 + O(|m| −1 ).…”
supporting
confidence: 74%
“…As in [3], we can prove that, if the cycle γ is sufficiently close to zero, then, under the substitution of Φ WKB into (4.8), the contribution O(l −∞ Φ WKB ) of the additional term…”
Section: Integral Representation Of Asymptotic Eigenfunctionsmentioning
confidence: 61%
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