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The quantum problem of an electron moving in a plane under the field created by two Coulombian centers admits simple analytical solutions for some particular inter-center distances. These elementary eigenfunctions, akin to those found by Demkov for the analogous three dimensional problem, are calculated using the framework of quasi-exact solvability of a pair of entangled ODEs descendants from the Heun equation. A different but interesting situation arises when the two centers have the same strength. In this case completely elementary solutions do not exist.
The problem of two fixed centers was introduced by Euler as early as in 1760. It plays an important role both in celestial mechanics and in the microscopic world. In the present paper we study the spatial problem in the case of arbitrary (both positi
We describe some basic tools in the spectral theory of Schrodinger operator on metric graphs (also known as quantum graph) by studying in detail some basic examples. The exposition is kept as elementary and accessible as possible. In the later sectio
The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L^2(R_+). Using
Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric f
We show that Tsirelsons problem concerning the set of quantum correlations and Connes embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchbergs QWEP conjecture) are essentially equivalent. Specifically,