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Additional info for A Determination of the Ratio of the Specific Heats of Hydrogen at 18 and -190C

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62) q(z)dz = s+ 1 π, 2 s = 0, 1, 2, . . , 1 2 ΛL ch04 January 30, 2008 B550 Stark Effect in a Hydrogenic Atom or Ion Phase-Integral Method 9in x 6in 51 where ΛL is a closed contour of integration encircling the origin and t but no other transiton points. 63) that one obtains the same quantization condition whether l = −1/2 or l = −1/2. It should, however, be emphasized that the motivation for the formulas, on which the quantization condition is based, is quite different in the cases when l = −1/2 and l = −1/2.

The phases of Q1/2 (η) indicated in the figure refer to the first Riemann sheet. 5c) ch05 January 30, 2008 B550 Stark Effect in a Hydrogenic Atom or Ion 9in x 6in Derivation of Phase-Integral Formulas 55 −Q 2 (η) η η1 0 ΛK η3 ΛL Q 1/2 = Q 1/2 0 Q 1 / 2 = −i Q 1 / 2 η1 η2 Fig. 1c. Qualitative behavior of −Q2 (η) for m = 0 in the super-barrier case. The wavy lines are cuts, and ΛL and ΛK are closed contours of integration. The part of ΛL that lies on the second Riemann sheet is drawn as a broken line.

14) ch03 January 30, 2008 B550 Stark Effect in a Hydrogenic Atom or Ion 9in x 6in Chapter 4 Phase-Integral Method Since the treatment in Chapter 5 is based on phase-integral formulas that are scattered in different publications, we collect in the present chapter background material that is necessary for reading Chapter 5. 1) dz 2 where R(z) is an unspecified analytic function of the complex variable z, involves the following items: (i) Arbitrary-order phase-integral approximation generated from an unspecified base function Q(z) as described in Chapter 1 of Fr¨ oman and Fr¨ oman (1996) and in Fr¨oman and Fr¨oman (2002); see also Dammert and P.

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A Determination of the Ratio of the Specific Heats of Hydrogen at 18 and -190C by Shields M. C.


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