SEMICLASSICAL QUANTIZATION OF THE MAGNETIC TOP

The magnetic top (A O. Barut, M. Bozic and Z. Maric: A nn. Phys. (N.Y. ), 214, (1992) 53) is quantized using the Bohr-Sommerfeld-Einstein (BS E) and the Einstein-Brillouin-Keller (EBK) quantization methods. It ha s been previously quantized by canonical, Schrodinger (A. O. Barut, M. Bozic and Z. Maric: Ann. Phys(N.Y.), 214, (1992) 53) and path-integra l methods (A. O. Barut and I. Duru: Phys. Lett. A, 158, (1991) 441). B y comparing the exact wave functions with the semi-classical ones, it is concluded that the usual conditions of quantization should be modif ied in order to allow for half-integer values of canonical angular mom entum (spin). This modification requires to abandon the condition of s ingle-valuedness of wave functions. We justify this using Pauli's and the Reiss argumentation that single-valuedness of wave functions does not follow from basic quantum-mechanical postulates and that a certain kind of multi-valued (i.e. path-dependent) wave functions cannot be e xcluded a priori.