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

Semiunitary transformation is applied to discuss upersymmetrization of cold Rydberg atoms. In the limit of vanishing kinetic energy the lowest angular momentum of the supersymmetric cold Rydberg atom is 3

In noncommutative spaces to maintain Bose–Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by generalizing one-particle quantum mechanics it is explored that the consistent ansatz of commutation relations of phase space variables should simultaneously include space–space non-commutativity and momentum–momentum non-commutativity, and a new type of boson commutation relations at the deformed level is obtained. Consistent perturbation expansions of deformed annihilation-creation operators are obtained. The influence of the new boson commutation relations on dynamics is discussed. The non-perturbation and perturbation property of the orbital angular momentum of two-dimensional system are investigated. Its spectrum possesses fractional eigen values and fractional intervals.

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.

The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic dipole of a cold Rydberg atom is arranged in appropriate electric and magnetic fields, so that the motion of the dipole is constrained to be planar and rotationally symmetric. Spatial noncommutativity leads the canonical angular momentum to possess fractional values. In the limit of vanishing kinetic energy, the dominate value of the lowest canonical angular momentum takes h=2. Furthermore, in the limit of eliminating the magnetic field, the dominate value of the lowest canonical angular momentum changes from h=2 to h=4. This result is a clear signal of spatial noncommutativity. An experimental verification of this prediction is suggested.