Phys. Rev. A 65, 042717 (2002) [6 pages]Nonrelativistic Levinson’s theorem in D dimensionsReceived 16 October 2001; revised 9 January 2002; published 1 April 2002 The Levinson theorem for the Schrödinger equation with a spherically symmetric potential in D dimensions is uniformly established by the Sturm-Liouville theorem. It is shown that the Levinson theorem for the cases without a half bound state does not depend on the spatial dimension D, namely, the phase-shift δl(0) of the scattering state with angular momentum l at zero momentum is equal to the total number nl of bound states multiplied by π. When a half bound state occurs the Levinson theorem may be modified. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.65.042717
DOI:
10.1103/PhysRevA.65.042717
PACS:
03.65.Nk, 73.50.Bk
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