Infinitely Strong Potential of Finite Rank

概要

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The scattering off a potential of finite rank (a sum of a finite number of separable potentials) is studied thoroughly in the neighborhood of infinity of potential strength; for this purpose we introduce the "strong coupling representation" by means of a canonical transformation. The same K matrix as for the infinitely strons repulsion is derived for the infinitely strong attraction. The difference between attraction and repulsion for a large but bite magnitude of strength call be understood in term of the effects from bound states and excited states which exist for attraction and repulsion, respectively. It is shown that this difference disappears from the K matrix at low energies as the potential strength tends to infinity. The high energy behavior of the phase shift shows a characteristic differerene between the two caw for a large but finite magnitude of strength. Levinson's theorem is discussed lucidly, and it is discussed how to interpret the identical result in the K matrix at infinity for both attraction ana repulsion.
理論物理学刊行会の論文
1966-12-00