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New approximation to the bound states of schrödinger operators with coulomb interaction
Author(s) -
Núñez Marco A.,
Izquierdo Gustavo B.
Publication year - 1994
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560520825
Subject(s) - bound state , coulomb , wave function , dirichlet distribution , schrödinger's cat , upper and lower bounds , computation , physical system , class (philosophy) , work (physics) , physics , mathematics , quantum mechanics , mathematical analysis , computer science , algorithm , artificial intelligence , boundary value problem , electron
In this work we present a mathematical formulation of the physical fact that the bound states of a quantum system confined into a box Ω (with impenetrable walls) are similar to those of the unconfined system, if the box Ω is sufficiently large , and it is shown how the bound states of atomic and molecular Hamiltonians can be approximated by those of the system confined for a box Ω large enough (Dirichlet eigenproblem in Ω). Thus, a method for computing bound states is obtained which has the advantage of reducing the problem to the case of compact operators. This implies that a broad class of numerical and analytic techniques used for solving the Dirichlet problem, may be applied in full strength to obtain accurate computations of energy levels, wave functions, and other physical properties of interest. © 1994 John Wiley & Sons, Inc.