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. 

The phase-integral method for solving differential equations of the 

We shall first briefly describe the phase-integral approximation referred to in item (i). Then we collect connection formulas pertaining to a single transition point [first-order zero or first-order pole of Q2(z) and to a real potential barrier, which can be derived by 

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We emphasize that the results obtained by us, as well as those obtained by the other authors quoted in this chapter, are obtained by neglecting the fine structure corrections. This is not a serious disadvantage for us, since our main intention has been to compare the accuracy obtainable by the phase-integral method with the accuracy obtainable by other methods of computation. For the experimental data corresponding to the theoretical values presented in this chapter we refer to the publications mentioned in this chapter. 

For large values of 112 (highly excited states of the r -equation) one can in general obtain more accurate values of E by the phase-integral method than by the numerical method used by Luc-Koenig and Bachelier (1980a), but for small values of ri2 the numerical method is in general more accurate. 

In Tables 8.10(c), 8.10(f) and 8.10(1) there are some states with very large fi -values for which the numerical method gives only an upper limit for T, while the phase-integral method gives a good value of T. 

Froman, N., and Froman, P. O., 2002, Physical Problems Solved by the Phase-Integral Method. Cambridge University Press. Paperback 2005. 

Treated by the Phase-Integral Method with Adjoined Papers by A Hokback and P 0 Froman... 

J. Heading, An Introduction to Phase-Integral Methods, Methnen s Monographs on Physical Subjects, London and New York, 1962. 

Dingle [4], whereas Patil [47] utilized the coalescence and inflexion properties of the wave function. Froman et al. [48] based their analysis on the phase-integral method. 

The results of one phase of the software lifecycle should be automatically passed on to the next phase integrated methods... 

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