The exact solutions of the N -dimensional Schrödinger equation with the Mie-type potentials are obtained using the conventional NikiforovUvarov method.The expectation values 〈r−1〉 and 〈r−2〉 and the virial theorem are also obtained in N -dimensions using the Hellmann-Feynman theorem.The ladder operators are also construct for the Mie-type potentials in N -dimensions and the matrix elements of so...

A virial theorem is established for the operator proposed by Brown and Ravenhall as a model for relativistic one-electron atoms. As a consequence, it is proved that the operator has no eigenvalues greater than max(mc, 2αZ− 1 2 ), where α is the fine structure constant, for all values of the nuclear charge Z below the critical value Zc: in particular there are no eigenvalues embedded in the esse...

A sum rule is derived for elastic scattering of hadrons at high energies which is in good agreement with experimental data on pp̄ available upto the maximum energy √ s = 2TeV . Physically, our sum rule reflects the way unitarity correlates and limits how large the elastic amplitude can be as a function of energy to how fast it decreases as a function of the momentum transfer. The universality of...

A planar phase space having both position and momentum noncommutativity is defined in a more inclusive setting than that considered elsewhere. The dynamics of a particle in a gravitational quantum well in this space is studied. The use of the WKB approximation and the virial theorem enable analytic discussions on the effect of noncommutativity. Consistent results are obtained following either c...

We look at the magnetisation of neutral atoms in large magnetic fields. Asymptotic formulas for the energy exist with high precision in different regions depending on how large the nuclear charge Z is compared to the magnetic field strength B. All these formulas take the splitting of the kinetic energy into Landau levels as the principal feature and then treat the electric potential as a pertur...

in the present work, a modified correlation is presented for the second virial coefficients of both polar and nonpolar fluids based on the corresponding states principle. the second virial coefficients of gaseous polar and non-polar compounds were calculated and compared with experimental data and with other correlations. comparisons with the existing correlations show that the present work is ...

This article synthesizes observational data from an extensive program aimed toward a comprehensive understanding of star formation in a low-mass star-forming molecular cloud. New observations and published data spanning from the centimeter wave band to the near infrared reveal the high and low density molecular gas, dust, and pre-main sequence stars in L1551. The total cloud mass of ∼ 160M cont...

A bstract We review and examine in detail recent developments regarding the question of nucleon mass decomposition. discuss particular virial theorem quantum field theory its implications for decomposition mechanical equilibrium. reconsider renormalization QCD energy-momentum tensor minimal-subtraction-type schemes physical interpretation components, as well role played by trace anomaly Poincar...

We evaluate the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 ...