The Schrodinger equation for stationary states in a central potential is
studied in an arbitrary number of spatial dimensions, say q. After
transformation into an equivalent equation, where the coefficient of the first
derivative vanishes, it is shown that in such equation the coefficient of the
second inverse power of r is an even function of a parameter, say lambda,
depending on a linear combination of q and of the angular momentum quantum
number, say l. Thus, the case of complex values of lambda, which is useful in
scattering theory, involves, in general, both a complex value of the parameter
originally viewed as the spatial dimension and complex values of the angular
momentum quantum number. The paper ends with a proof of the Levinson theorem in
an arbitrary number of spatial dimensions, when the potential includes a
non-local term which might be useful to understand the interaction between two
nucleons.Comment: 17 pages, plain Tex. The revised version is much longer, and section
5 is entirely ne
