Restricted quantum-mechanical three-body problems. II - A general theory of helium-like ions

Mathematics

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Ion Motion, Perturbation Theory, Quantum Mechanics, Three Body Problem, Boundary Conditions, Boundary Value Problems, Differential Equations, Scalars, Schroedinger Equation, Singularity (Mathematics), Wave Functions

Scientific paper

A new method is presented in a general form to solve the Schroedinger equation of helium-like ions. The wave function is expanded in terms of the eigenfunctions of a moving electron in the field of two Coulombic ions which are fixed in space. This makes the method similar to the Dirac perturbation theory (perturbation theory for time-dependent problems). In the present method an infinitely coupled system of infinitely many second-order ordinary differential equations must be solved instead of one second-order partial differential equation of three variables. The nature of the singular points and boundary conditions are discussed and some general relations are given which are useful for the numerical treatment.

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