Vol. 15, No. 2, 1965

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On the phase-shift formula for the scattering operator

Teruo Ikebe

Vol. 15 (1965), No. 2, 511–523

Let us denote by S|k| the scattering operator attached to a fixed value |k|2 of the kinetic energy. We shall show by a method different from that of Buslaev [2] that S|k| is the identity plus a Hilbert-Schmidt integral operator under a weaker assumption on q(x), and give a way of unique determination of the phase shifts in terms of which S|k| can be represented as the orthogonal direct sum of multiplication operators by a number with absolute value equal to unity.

Mathematical Subject Classification
Primary: 81.47
Received: 20 December 1963
Published: 1 June 1965
Teruo Ikebe