Inst High Energy Phys, Beijing 100039, Peoples R China
; Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Mexico City 04510, DF, Mexico
; China Ctr Adv Sci & Technol, World Lab, Beijing 100080, Peoples R China
The Levinson theorem for the Schrodinger 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 delta(l)(0) of the scattering state with angular momentum l at zero momentum is equal to the total number n(l) of bound states multiplied by pi. When a half bound state occurs the Levinson theorem may be modified.