相关论文: Sum rules for Confining Potentials
It is shown that it is possible to establish sum rules that must be satisfied at the nodes and extrema of the eigenstates of confining potentials which are functions of a single variable. At any boundstate energy the Schroedinger equation…
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…
We apply quantum mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, $V(x) = V(-x)$, and their parity-restricted partners, ones…
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…
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…
We derive spectral sum rules for inverse powers of the eigenvalues of the Helmholtz equation on a $d$-sphere in the presence of an arbitrary density. By adopting a rigorous renormalization scheme, we remove the divergent contributions of…
In connection with recent publications we discuss spectral sum rules for the Tomonaga-Luttinger model without using the explicit result for the one-electron Green's function. They are usefull in the interpretation of recent high resolution…
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…
The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a microscopic derivation of these sum rules in the sector of…
An approach is suggested defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed.…
It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of…
Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green's functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning…
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…
The power series method has been adapted to compute the spectrum of the Schrodinger equation for central potential of the form $V(r)={d_{-2}\over r^2}+{d_{-1}\over r}+\sum_{i=0}^{\infty} d_{i}r^i$. The bound-state energies are given as…
The Coulomb gauge model of QCD is studied with the introduction of a confining potential into the scalar part of the vector potential. Using a Green function formalism, we derive the self-energy for this model, which has both scalar and…
The validity of the Luttinger sum rule is considered for finite systems of interacting electrons, where the Fermi volume is determined by location of zeroes of Green's function. It is shown that the sum rule in the paramagnetic state is…
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…
In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also…
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…