Operator (computer programming)

About: Operator (computer programming) is a research topic. Over the lifetime, 40896 publications have been published within this topic receiving 671452 citations. The topic is also known as: operator symbol & operator name.

Fundamental properties of Hamiltonian operators of Schrödinger type

Abstract: Introduction. The fundamental quality required of operators representing physical quantities in quantum mechanics is that they be hypermaximal(l) or self-adjoint(2) in the strict sense employed in the theory of Hilbert space, which is equivalent to saying that the eigenvalue problem is completely solvable for them, that is, that there exists a complete set (discrete or continuous) of eigenfunctions. It will, therefore, be one of the important problems of mathematical physics to show that this is actually the case for all operators appearing in current structure of quantum mechanics, for the self-adjointness of an operator is a property requiring careful separate consideration and by no means a direct consequence of its Hermitian symmetry [cf. (S), chap. X]. The problem has, of course, been solved in the case of operators for which the eigenvalue problem is explicitly solved by separation of variables or other methods, but it seems not to have been settled in the general case of manyparticle systems('). The main purpose of the present paper is to show that the Schrodinger Hamiltonian operator(4) of every atom, molecule, or ion, in short, of every system composed of a finite number of particles interacting with each other through a potential energy, for instance, of Coulomb type, is essentially selfadjoint(5) (6) . Thus our result serves as a mathematical basis for all theoretical works concerning nonrelativistic quantum mechanics, for they always pre-

A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications

Abstract: In this paper we present a comprehensive account of a manifestly size-consistent coupled cluster formalism for a specific state, which is based on a reference function composed of determinants spanning a complete active space (CAS). The method treats all the reference determinants on the same footing and is hence expected to provide uniform description over a wide range of molecular geometry. The combining coefficients are determined by diagonalizing an effective operator in the CAS and are thus completely flexible, not constrained to preassigned values. A separate exponential-type excitation operator is invoked to induce excitations to all the virtual functions from each reference determinant. The linear dependence inherent in this choice of cluster operators is eliminated by invoking suitable sufficiency conditions, which in a transparent manner leads to manifest size extensivity. The use of a CAS also guarantees size consistency. We also discuss the relation of our method with the extant state-specific...

Sur le spectre des opérateurs aux différences finies aléatoires

Abstract: We study a class of random finite difference operators, a typical example of which is the finite difference Schrodinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schrodinger operator with a random potential has pure point spectrum and developps no static conductivity.