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Reference17 articles.
1. F. Calogero:Variable-Phase Approach to Potential Scattering (New York, 1967), pp. 185–189.
2. R. G. Newton:Journ. Math. Phys.,1, 319 (1960). We shall follow the notation of this article. Moreover, we choose the units such that ħ=2M=1, so that the energy is given byE=k 2,k being the wave number.
3. R. G. Newton:Scattering Theory of Waves and Particles (New York, 1966). Notice the change of notationk→−k from the preceding article to this book.
4. K. Meetz:Journ. Math. Phys.,3, 690 (1961). Notice that we assumeV(r) to be positive everywhere. Notice also the change of notationg→−λ (so that the bound states correspond here to λ>0) andk 2→s. The fact that making the potential more attractive (g more negative) makes the binding energies larger (E more negative) is clear from eq. (5.3) of this paper, which gives in our notation (dg/dE)>0. This can also be seen by analogy with the motion of Regge poles,i.e. zeros off l (k, g),greal and fixed,l complex. From the radial Schrödinger equation, the analogy betweeng andl(l+1) is clear. For details, seeR. G. Newton:Journ. Math. Phys.,3, 867 (1962), eq. (4.3), and footnote (12) thereof.
5. Forl=0, the end point −g 0 should not be included since we cannot have a bound state with zero binding energy in theS-wave (2,3).
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