Related papers: Sum rules and the domain after the last node of an…
Using the Green's function associated with the one-dimensional Schroedinger equation it is possible to establish a hierarchy of sum rules involving the eigenvalues of confining potentials which have only a boundstate spectrum. For some…
The nucleon spectral function in nuclear matter fulfills an energy weighted sum rule. Comparing two different realistic potential, these sum rules are studied for Green's functions that are derived self-consistently within the $T$ matrix…
Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been…
We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order $N$ may be obtained in terms of a diagrammatic…
The neutron and proton single-particle spectral functions in asymmetric nuclear matter fulfill energy weighted sum rules. The validity of these sum rules within the self-consistent Green's function approach is investigated. The various…
A general quantization rule for bound states of the Schrodinger equation is presented. Like fundamental theory of integral, our idea is mainly based on dividing the potential into many pieces, solving the Schr\"odinger equation, and…
Apparent inconsistencies between different formulations of nucleon sum rules at finite density are resolved through a proper accounting of asymmetries in the spectral functions between positive- and negative-energy states.
We establish a set of exact sum rules that relate the interatomic force constants to the frequency-dependent electromagnetic susceptibility of a solid or molecule, thereby generalizing the long-established principles of rototranslational…
We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation…
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…
Green's functions for reflectionless potentials are constructed and analyzed. Green's functions for power law potentials, their Super Symmetric partners and sum rules for eigenvalues are examined. The SUSY partner potentials to power law…
The problem of a particle localized in a ultra-short potential in one dimension is considered. By proposing a general solution to Schrodinger;s equation we show that the energy spectra and the probability of the particle have definite…
We present a polymer quantization of the -lambda/r^2 potential on the positive real line and compute numerically the bound state eigenenergies in terms of the dimensionless coupling constant lambda. The singularity at the origin is handled…
We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j \pm 1| and…
We derive non-perturbative sum rules in SU($N$) lattice gauge theory at finite temperature. They relate the susceptibilities of the trace anomaly and energy-momentum tensor to temperature derivatives of the thermodynamic potentials. Two of…
The paper considers the properties of pseudo stationarity in a broad sense and pseudo strong mixing for sequences of random variables corresponding to arithmetic functions. Assertions on this topic have been proven. The implementation of…
Weak-coupling conserving approximations can be constructed by truncations of the Luttinger-Ward functional and are well known as thermodynamically consistent approaches which respect macroscopic conservation laws as well as certain sum…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
We derive sum rules among scalar masses for various boundary conditions of the hidden-visible couplings in the presence of hidden sector dynamics and show that they still can be useful probes of the MSSM and beyond.
Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems,…