[en] The virial theorem for transverse MHD flows is derived, and the necessary condition for the existence of stable equilibrium is obtained. This condition for monatomic gases implies a result which contradicts earlier work of Chandrasekhar and Fermi [Astrophys. J. 118, 116 (1953)]

[en] Published in summary form only

[en] We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)

No abstract available

[en] If the exact electron density of an atom or molecule is known, how accurately can we estimate the energy? The virial of the density yields exactly E_xc + T_c, where E_xc is the exchange-correlation energy and T_c is the correlation contribution to the kinetic energy, while local and gradient-corrected (e.g., PW91) density functional approximations are more accurate for the combination E_xc-T_c than for E_xc alone. Combining these two improves the accuracy of the energy by a factor of two or three exclamation point

[en] A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann–Feynman theorem produces the final statement of the virial theorem. (paper)

[en] Everything you always wanted to know about quantum-mechanical virial theorems but did not dare to ask. 8 refs. (Authors)

[en] A Hamiltonian formulation of hydrodynamics is well known for the case of purely irrotational flows and it now exists in a more general case as well. The minimal extension of the action principle is obtained from two axioms: 1. That the number of independent degrees of freedom be 4, as in standard hydrodynamics. 2. That the equation of continuity must be one of the Euler-Lagrange equations, and that it allows for vorticity. Applications include: 1. Couette flow with a new criterion for the breakdown of laminar motion. 2. A rotating source for Einstein’s equation that respects the Bianchi identity. 3. A new approach to the electromagnetism of fluids. 4. A rigorous virial theorem for fluids. 5. A critique of the current state of the theory of atmospheres.

No abstract available

[en] Usually the Virial theorem, which can be derived from the Feynman-Hellmann theorem, applies to Hamiltonians without coordinates-momentum coupling. In this paper we discuss when there are such kind of couplings in Hamiltonians then how the Virial theorem should be modified. We also discuss the energy contribution arising from the coordinates-momentum coupling for a definite energy level