qDeformed Dynamics and Virial Theorem.pdfVIP

q-Deformed Dynamics and Virial Theorem 2 0 0 2 Jian-zu Zhanga,b,§ y a M 4 1 a Institute for Theoretical Physics, Box 316, East China University of Science and 1 v Technology, Shanghai 200237, P. R. China 5 2 b Department of Physics, University of Kaiserslautern, PO Box 3049, D-67653 1 5 Kaiserslautern, Germany 0 2 0 / h t - p Abstract e h In the framework of the q-deformed Heisenberg algebra the investigation of q- : v deformation of Virial theorem explores that q-deformed quantum mechanics possesses i X better dynamical property. It is clarified that in the case of the zero potential the r theoretical framework for the q-deformed Virial theorem is self-consistent. In the a selfadjoint states the q-deformed uncertainty relation essentially deviates from the Heisenberg one. § E-mail address: jzzhang@physik.uni-kl.de jzzhangw@online.sh.cn In hunting new physics at extremely high energy scale clarifying modification of the ordinary quantum mechanics at extremely small space scale is important. The ordinary quantum mechanics is based on the Heisenberg commutation relation. From the space scale 10−8 cm down to, according to the present test of quantum electrodynamics, at least 10−18 cm every test confirms that the Heisenberg commutation relation is correct. There is a possibility that the Heisenberg commutation relation at extremely short dis- tances much smaller than 10−18 cm may need to be modified. In search for such possibility q-deformed quantum mechanics is a