Related papers: Recurrence relations for relativistic two centre m…
Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
Stable recursive relations are presented for the numerical computation of the integrals $$\int d{\bf r}_1 d{\bf r}_2 r_1^{l-1} r_2^{m-1} r_{12}^{n-1} \exp{\{-\alpha r_1 -\beta r_2 -\gamma r_{12}\}}$$ ($l$, $m$ and $n$ integer, $\alpha$,…
In this paper we present a simple method for deriving recurrence relations and we apply it to obtain two equations involving the Lerch Phi function and sums of Bernoulli and Euler polynomials. Connections between these results and those…
We develop the systematics for applying operators on Minkowski correlation functions to get the inflationary correlation functions. Simple structures and recursion relations are known for Minkowski correlation functions. Using the operator…
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…
We consider polynomials that are defined as Wronskians of certain sets of Hermite polynomials. Our main result is a recurrence relation for these polynomials in terms of those of one or two degrees smaller, which generalizes the well-known…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation…
This article suggests that thinking about the role of reference frames can provide new insight into Extended Wigner's Friend scenarios. This involves appealing to symmetries to make a principled distinction between properties of a system…
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed.…
We present an exact formula for the computation of the interference rate of radiation in the case of two charges revolving with constant angular velocity at opposite ends of a diameter in a fixed circle. The formula is valid for arbitrary…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
In this work we study the Schr\"{o}dinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter of…
Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such…
From the matrix point of view, we use the recursion to discuss four combinatorial numbers in terms of the integer lattice paths, this is different from Andr\'a's method (Andra). We give four tables and matrices, and their relations, and…
An algebraic interpretation of the one-variable quantum $q$-Krawtchouk polynomials is provided in the framework of the Schwinger realization of $\mathcal{U}_{q}(sl_{2})$ involving two independent $q$-oscillators. The polynomials are shown…
Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and…