International Centre for Theoretical Physics More about the Q-deformed H-atom Wave Functions: Normal and Abnormal Series International Atomic Energy Agency United Nations Educational, Scientific and Cultural Organization

The 3-dim quantum Euclidean space and the q-deformed Schrodinger equation are further investigated. The reality condition is taken into account by introducing the right derivatives as well as the left ones. It seems that from the properties of the ^-derivatives, corresponding to a fixed "energy level" there are infinitive numbers of q deformed wave functions. Among them only one belongs to the normal series, its radial wave function (rwf) has the same number of nodes as that of its classical counterpart. All others have more nodes in their rwf s, and then fall into the abnormal aeries. This is illustrated by solving the ij-Schrodinger equation explicitly for the s-wave solutions. MIRAMARE TRIESTE January 1994 'Permanent address: Department of Physics, Peking University, Beijing 100871, People's Republic of China.