By Gordon W. F. Drake
Industry: Graduate scholars and execs in atomic, molecular, and optical physics, in addition to these in condensed subject and plasma physics, chemistry, and engineering. This crucial new source from AIP Press is the 1st unmarried quantity to bridge the numerous interrelated disciplines of atomic, molecular, and optical (AMO) physics. in addition to a precis of key rules, strategies, and effects, many chapters give you diagrams of kit, graphs, and desk of knowledge. From atomic spectroscopy to purposes in comets, you will discover contributions from over a hundred authors, all leaders of their respective disciplines. on hand on CD- ROM
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12) Hnr (ξ) exp −ξ 2 /2 . √ Here once more notation is introduced ξ ≡ nω (r − r0 ) . According to Eq. 10), the unperturbed harmonic oscillator has the frequency ω0 = nω. In the region of localization of a particle the typical deviations of this particle from the equilibrium point are small: −1/2 (r − r0 ) ∼ ω0 ∼ n −1/2 1. Analogous estimates are valid for deviations of radial coordinate in anharmonic terms which can be considered as small perturbation of the harmonic oscillator. We write this perturbation in the form of sum of two terms: one term is even function of the variable x ≡ r − r0 while the other term is odd function of this variable V = V (+) + V (−) ; V (+) (x) = 2r12 nr (nr + 1) − 23 n (2nr + 1) 0 V (−) (x) = (2nr + 1) n rx3 + n 2 αx 3 .
However, we should substitute g by g0 and put ε(0) = 0. Hence, we obtain g0 = − 1 ; r0 v (r0 ) = −2v(r0 ). 36) (1) The first approximation can be found from Eq. 12) by formal substitution εnr → −g1 v(r0 ). Taking into account Eq. 36), we obtain g1 = − 2nr + 1 1 ω− 2 2v(r0 ) r0 = (2nr + 1) ωr02 − 1 g0 . 37) Here, the frequency ω is given by Eq. 11), but with substitution g → g0 . 13)). Taking it into account, we obtain g2 = 15 22 ω 3 + s A2 − (2 + s) B v (r0 ) 16 15 8 √ 1+s 1 s 6A C + 5C + 1 − − C+ 8 4 C .
The condition of applicability of WKB approximation is fulfilled for Rydberg states on the radial dimensions r aB = 2 m e Z e2 . 4) for electron energy allows to neglect the dependence of the quantum defect on the principal quantum number n. 1 Obtain the energy spectrum, Eq. 1) of Rydberg states of atoms using WKB wave function, Eq. 3). 3) corresponds to taking into account the boundary condition at r → 0 in the exact radial wave function, where Eq. 3) is inapplicable. The boundary condition in the infinity, r → ∞, is Rnl (r ) → 0.
Atomic, Molecular, & Optical Physics Handbook by Gordon W. F. Drake