Abstract
IT has recently been pointed out by Kramers and Heisenberg1 that from the knowledge of the collision cross-sections between free particles, the energy-levels of the discrete states can be deduced. For this purpose the asymptotic wave function in the continuous spectrum (for one particle under the influence of a fixed centre of force), is considered, where Sl is the diagonal form of the S-matrix and a function of the real momentum k. The stationary states follow then from the condition k = ix, and and, for relativistic particles, It is evidently necessary that x < m. The upper half of the k-plane (x < 0) gives only a repetition of the same physical facts if the roles of zeros and poles of S are interchanged.
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References
Several as yet unpublished papers by Heisenberg. A complete account of them is given by Møller, ref. 2.
Møller, Kgl. Danske Vid. Sels. Math-Fys. Medd., 23, No. 1 (1945); 22, No. 19 (1946); Nature, 158, 403 (1946).
Heitler and Hu, Proc. Roy. Irish Acad., in the press.
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HEITLER, W., HU, N. Interpretation of Complex Roots of the S-Matrix. Nature 159, 776–777 (1947). https://doi.org/10.1038/159776a0
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DOI: https://doi.org/10.1038/159776a0
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