In the framework of the q-deformed Heisenberg algebra the investigation of q-deformation of Virial theorem explores that q-deformed quantum mechanics possesses better dynamical property. It is clarified that in the case of the zero potential the theoretical framework for the q-deformed Virial theorem is self-consistent. In the selfadjoint states the q-deformed uncertainty relation essentially deviates from the Heisenberg one.

Characteristics of Abelian dyon-fermion bound system, parity-violating effects, a new series of energy spectra, effects related to the non-vanishing electric dipole moment, feature of spin orientation etc., are analyzed and compared with hydrogen-like atom. These analyses explore possibility of a new approach of searching for dyons under bound condition.

Corresponding to two ways of realizing the q-deformed Heisenberg algebra by the undeformed variables there are two q-perturbative Hamiltonians with the additional momentum-dependent interactions, one originates from the perturbative expansion of the potential, the other originates from that of the kinetic energy term. At the level of operators, these two q-perturbative Hamiltonians are different. In order to establish a reliable foundation of the perturbative calculations in q-deformed dynamics, except examples of the harmonic-oscillator and the Morse potential demonstrated before, the general q-perturbative equivalent theorem is demonstrated, which states that for any regular potential which is singularity free the expectation values of two q-perturbative Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent. For the q-deformed "free" particle case, the perturbative Hamiltonian originated from the kinetic energy term still keeps its general expression, but it does not lead to energy shift.

The energy spectrum of q-deformed Schrodinger equation is demonstrated. This spectrum includes an exponential factor with new quantum numbers, the q-exciting number and the scaling index. The pattern of quark and lepton masses is qualitatively explained by such a q-deformed spectrum in a composite model. q2000 Elsevier Science B.V. All rights reserved.

Within a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr