By Sydney Geltman

ISBN-10: 1483230678

ISBN-13: 9781483230672

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20) is valid. 19) are integrated over all k space, the right-hand side becomes 1. 3) is sub stantiated. An identical proof would also apply to ^r0i^*(r)^k»=S(k'-k). 23) 39 Part L Static Field Scattering 5b. 24) Ό^ never becomes negligible asymptotically compared with the centrifu gal barrier, /(/ + l ) / r 2 . This differential equation will therefore not have solutions which ~:;r^ ún(kr — \1'π + τ/^), nor become a linear com bination of the rji and rn¿ functions. 24) for the bound, negative energy states of the hydrogen atom is very familiar.

REFERENCES 1. M . Abramowitz and I. A. ), ^'Handbook of Mathematical F u n c t i o n s , " Chapters 6 and 13 (Natl. Bur. S t d . A p p l . M a t h . Ser. 55). U . S . G o v t . Printing Office, Washington, D . C . , 1964. 2. H . A. Bethe and E. E. a. Springer, Berlin (Academic Press, N e w York), 1957. 44 6. Integral Equation Formulation 6. INTEGRAL EQUATION FORMULATION In solving the Schrödinger equation for scattering we had to impose the correct physical asymptotic conditions on the wave function.

An upper limit on d-qijdk or {Δ{)ι does not exist. This result is consistent with the behavior of τ; ^ in passing through a narrow resonance. In Fig. 5 we see that dηι|dk, and hence {Δΐ)ι ^ are very large. Thus, scattering at such a resonance energy means that the incident particle spends a long time in the vicinity of the target. 21) in which ηι decreases by ττ is a mathematical result of a resonance state lying near but below the real k axis. Such resonance states are physically not possible for the reason given above, as well as the other previously stated result that the only zeros of f^{k) lying below the real axis are the bound states.

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