Related papers: On certain sum rules for the hydrogen atom

We provide a brief summary of the observed sum rule anomalies in the high-T$_c$ cuprate materials. A recent issue has been the impact of a non-infinite frequency cutoff in the experiment. In the normal state, the observed anomalously high…

We discuss the boundary effects on a quantum system by examining the problem of a hydrogen atom in a spherical well. By using an approximation method which is linear in energy we calculate the boundary corrections to the ground-state energy…

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections…

In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…

The importance of the nonlinear corrections on the momentum sum rule is investigated on the initial scale $Q_{0}^2$. Nonlinear corrections are found to play an indispensable role in the singlet and gluon momentum sum rule in the high-order…

It is shown that, Baire generically, the bound states of the Hamiltonian of the Hydrogen atom have spectral measures with exact $0$-lower and $1/3$-upper generalized fractal dimensions; the relation to (a weak form of) dynamical…

It is shown that the functional form of the equation of state of [4-8] is not correct in general case.

We study the corrections to the fine-structure constant from the generalized uncertainty principle in the spacetime of a domain wall. We also calculate the corrections to the standard formula to the energy of the electron in the hydrogen…

We discuss the extraction of form factors from three-point sum rules making use of harmonic-oscillator model, where we derive the exact expression for the relevant correlator. We determine the form factor of the ground state by the standard…

Sum rules are derived relating mean squared charge radii of the pseudoscalar mesons with the convergent integral of the difference of hadron photoproduction cross-sections on pseudoscalar mesons.

We show that the authors of the commented paper draw their conclusions from the eigenvalues of truncated Hamiltonian matrices that do not converge as the matrix dimension increases. In one of the studied examples the authors missed the real…

We generalize forward real Compton amplitude to the case of the interference of the electromagnetic and weak neutral current, formulate a low-energy theorem, relate the new amplitudes to the interference structure functions and obtain a new…

We show that for multi-orbital quantum impurity models the non-crossing approximation and one-crossing approximation versions of the self-consistent hybridization expansions violate the sum rules relating the coefficients of the…

This work is a companion paper of Gamboa, Nagel, Rouault (J. Funct. Anal. 2016). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned…

The Drell-Hearn-Gerasimov (DHG) sum rule relates the helicity structure of the photoabsorption cross section to the anomalous magnetic moment of the nucleon. It is based on Lorentz and gauge invariance, crossing symmetry, causality and…

Hydrogen atom is studied as a quantum-classical hybrid system, where the proton is treated as a classical object while the electron is regarded as a quantum object. We use a well known mean-field approach to describe this hybrid hydrogen…

We derive general expressions for the sum rules of the eigenvalues of drums of arbitrary shape and arbitrary density, obeying different boundary conditions. The formulas that we present are a generalization of the analogous formulas for one…

We generalize a forward light-by-light scattering sum rule to the case of heavy quarkonium radiative transitions. We apply such sum rule to the bottomonium states, and use available data on radiative transitions in its evaluation. For the…

Graviton absorption cross sections and emission rates for hydrogen are calculated by both semi-classical and field theoretic methods. We point out several mistakes in the literature concerning spontaneous emission of gravitons and related…

The gradient expansion of the kinetic energy functional, when applied for atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the…